The decay behaviors of the molecule state have been studied in an effective Lagrangian approach. We find that the molecule state dominantly decays into and 3c6563069365364f6a7a1a771d" title="Click to view the MathML source">ηcη. The total and partial widths are strongly dependent on the model parameter, however, the ratio of the partial widths for 3c6563069365364f6a7a1a771d" title="Click to view the MathML source">ηcη and is relatively stable and predicted to be about c000e8c84089322ade79077326f358" title="Click to view the MathML source">0.17∼0.22. In addition, our evaluation shows that the partial width for the molecule to J/ψω is too small to be observed, thus the charmonium-like state X(3915) should not be a molecule state.