A quadratic scalar and vector coupling model proposed recently has been applied to finite nuclei.The calculated results are compared with those of the derivative scalar coupling (DSC) model and the nonlinear Walecka model The results show that the spin-orbit splittings are improved considerably by quadratic couplings in contrast to the DSC model However,the binding energy per nucleon,rms charge radius,as well as the spin-orbit splittings in the quadratic model are still small compared with those given by the nonlinear Walecka model and the experimental data.