We present a study of the molecular beam epitaxy of InP nanowires (NWs) on (001) oriented SrTiO3 (STO) substrates using vapor liquid solid mechanism and gold-indium as metal catalyst. The growth direction of InP NWs grown on STO(001) is compared with NWs grown on (001) and (111) oriented silicon substrates. Gold-indium dewetting under a flux of indium results in the majority of InP NWs growing vertically from the surface of STO(001). With the growth parameters we have used the NWs have a pure wurtzite structure and are free of stacking faults and cubic segments. The structural quality of the NWs is confirmed by micro-photoluminescence measurements showing a narrow peak linewidth of 6.5 meV.