The modified LindstedtPoincaré method modifies the expansion of the fundamental frequency based on the classical LP method, and the convolution integral method provides an iteration scheme to obtain the asymptotic solution. Firstly, we obtained the second order solutions of a quadratic nonlinear oscillator respectively by these two methods, and demonstrated that the solution obtained by convolution integral was uniformly convergent. Secondly, a technique of numerical order verification was applied to verify that the asymptotic solutions were uniformly valid for small parameter. Finally, numerical comparison of error shows that this two methods are invalid for large parameter. So, these two methods are limited by small parameter when they are applied to quadratic nonlinear oscillator.