We investigate a scalar field dark energy model (i.e., ϕ CDM model) with massive neutrinos, where the scalar field possesses an inverse power-law potential, i.e., science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si1.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=d4c12d6502c7346b91dfadabd7ad642c" title="Click to view the MathML source">V(ϕ)∝ϕ−α (science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si2.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=001c4704f51e0c60dead687a997f3942" title="Click to view the MathML source">α>0). We find that the sum of neutrino masses science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si3.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=63615ab8838ba01c685578e49361bc02" title="Click to view the MathML source">Σmν has significant impacts on the CMB temperature power spectrum and on the matter power spectrum. In addition, the parameter α also has slight impacts on the spectra. A joint sample, including CMB data from Planck 2013 and WMAP9, galaxy clustering data from WiggleZ and BOSS DR11, and JLA compilation of Type Ia supernova observations, is adopted to confine the parameters. Within the context of the ϕ CDM model under consideration, the joint sample determines the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the Thomson scattering optical depth due to reionization, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si4.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=bda79ad2d2fc5043b3a81ad704a685f9">, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si5.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=fbc04c98c4afceb565f5db5340d04deb">, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si6.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=2e7cf3362b3717c42456d3841bab3da3" title="Click to view the MathML source">Ωbh2=0.0222±0.0005, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si7.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=5eef44b4fadd6ea43523c492ebeb41f1" title="Click to view the MathML source">Ωch2=0.1177±0.0036, and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si8.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=82951e6a26a2564b22d48675657545ce">, respectively, at 95% confidence level (CL). It turns out that i9" class="mathmlsrc">science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si9.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=d3e1aa9187da6b34ba803f4ecc736da8" title="Click to view the MathML source">α<4.995 at 95% CL for the ϕ CDM model. And yet, the ΛCDM scenario corresponding to science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si10.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=2167b4dbdf2bfb28d5a4b18bc194b9d1" title="Click to view the MathML source">α=0 is not ruled out at 95% CL. Moreover, we get science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si11.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=0b52cb64811698d8801b522333bf04c8" title="Click to view the MathML source">Σmν<0.262 eV at 95% CL for the ϕ CDM model, while the corresponding one for the ΛCDM model is science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si12.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=b536cb5baf7bf6875dc583a0c1be75d9" title="Click to view the MathML source">Σmν<0.293 eV. The allowed scale of science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si3.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=63615ab8838ba01c685578e49361bc02" title="Click to view the MathML source">Σmν in the ϕCDM model is a bit smaller than that in the ΛCDM model. It is consistent with the qualitative analysis, which reveals that the increases of α and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si3.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=63615ab8838ba01c685578e49361bc02" title="Click to view the MathML source">Σmν both can result in the suppression of the matter power spectrum. As a consequence, when α is larger, in order to avoid suppressing the matter power spectrum too much, the value of science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315008709&_mathId=si3.gif&_user=111111111&_pii=S0370269315008709&_rdoc=1&_issn=03702693&md5=63615ab8838ba01c685578e49361bc02" title="Click to view the MathML source">Σmν should be smaller.