$La_{0.5}Sr_{0.5}CoO_3$ (LSCO) electrode thin films with a resistivity of ~ 1,600 ${mu}{Omega}cm$ were grown on c-$Al_2O_3$ (0001) substrate. $ZnSnO_3$ (ZTO) thin films with different thicknesses were directly grown on LSCO/c-$Al_2O_3$ (0001) substrates at a substrate temperature that ranged from 550 to $750^{circ}C$ using Pulsed Laser Deposition (PLD). The secondary phase $Zn_2SnO_4$ occurred during the growth of ZTO films and it became more significant with further increasing substrate temperature. Polarization-electric-field (P-E) hysteresis characteristics, with a remnant polarization and coercive field of 0.05 ${mu}C/cm^2$ and 48 kV/cm, respectively, were obtained in the ZTO film grown at $700^{circ}C$ in 200 mTorr.