Using the various exchange-correlation functionals, such as LDA, GGA-PBE, GGA-PBEsol and GGA-AM05 functionals, first principle studies were conducted to determine the structures of paraelectric and ferroelectric PbTiO3. Based on the structures determined by the various functionals, the piezoelectric properties of PbTiO3 are predicted under the density-functional perturbation theory (DFPT). The present prediction with the various GGA functionals are closer to the experimental findings compared to the LDA values. The present DFT calculations using the GGAPBEsol functional estimate the experimental data more reasonably than the conventional LDA and GGA fucntionals. The GGA-AM05 functional also predicts the experimental data as well as the GGA-PBEsol. The piezoelectric tensor calculated with PBEsol is relatively insensitive to pressure.