Efficient interatomic potential for PbTiO_3 crystals, which are intensively applied to ferroelectric devices, is required for the atomic-scale study of mechanical and electronic behavior of the materials. In this study, we develop parameters of empirical shell-model potential functions for the equilibrium lattice parameters, elastic constants, Born effective charges and phonon dispersion relations of both cubic and tetragonal PbTiO_3 by fitting to ab initio results using the Newton-Raphson method. The optimized potential for PbTiO_3 reproduces the structures, elastic properties and phonon dispersion relations in good accuracy, whereas Born effective charges are poorly reproduced.