To improve the trajectory optimization with Chebyshev local collocation method, we study the convergence and stability of Chebyshev local collocation method and provide a theoretical basis for its application. In this paper, the examples of Hyper-sensitive and Minimum-energy problem verify the feasibility and effectiveness of Chebyshev local collocation method which not only is convergent and stable for Hyper-sensitive problem, but also can achieve higher accuracy and faster computation speed in some degree compared with traditional interpolation method and even classic Chebyshev pseudospectral method.