The stability of singular points and their trajectories in phase space of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are studied. Firstly, the singular points of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are obtained. Based on the Lyapunov indirect method and the gradient method, the stability of equilibrium points of this system are then discussed. Finally, numerical simulations are performed by the software Matlab, and Poincare surface of the section are used to study the trajectories of the system in phase space. It is found that, with the increase of energy, the chaos appears finally through two stages of regular motion as well as the coexistence of regular motion and chaos.