The closed-orbit bifurcation of a two-dimensional system with parameters was discussed. Based on the successor function method, the limit cycle of the system near the equilibrium point was got. Using the curve coordinate transformation to the system, we find its successor function, and then received several limit cycles. By the aid of curvilinear coordinate transformation, we got the subsequent function of the system, and analyzed the stability of the limit cycles with the parameters from scratch to existence. Finally, numerical simulations were carried out.