In this paper, a new method was proposed for solving two-dimensional nonlinear elliptic-parabolic interface problems with nonhomogeneous jump conditions. The method we used is a finite elementmethod coupledwith Newton’s method. It is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the L∞ norm for different kinds of nonlinear terms and interface with complicated geometry.