Single crystalline PbTiO3 films have been epitaxially grown on SrTiO3 (001) substrates by molecular beam epitaxy using H2O2 as the source of active oxygen. The optimum growth conditions have been determined by analyzing a range of growth parameters affecting growth and used to attain single phase and stoichiometric PbTiO3 thin films. In situ reflection high-energy electron diffraction pattern indicated the PbTiO3 films to be grown under a two-dimensional growth mode. The full width at half maximum of the rocking curve of a relatively thin 65 nm (001) PbTiO3 film is 6.2 arc min which is indicative of high crystal quality. The band gap of PbTiO3, as determined by ellipsometric measurement, is 3.778 eV.