This paper studied the asymptotic solutions of non-linear systems with the field method combining with the method of multiple time scales. A state variable in the state equation was regarded as a field function of another state variable and time, then the original system was reduced to the basic equation with initial conditions. Expanding the original equation, we solved step by step the perturbation equations and obtained the first approximate differential equations of the amplitude and phase. As an example, the first analytical solutions of non-linear systems were found,which agreed with the numerical solutions.