In this paper, we present a new method for solving a singular nonlinear second-order periodic boundary value problem. Its analytical solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation u_n(x) to the analytical solution u(x) is obtained and is proved to converge to the analytical solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.