A robust constant thrust rendezvous approach under thrust failure is proposed based on the relative motion dynamic model. Firstly, the design problem is cast into a convex optimization problem by introducing a Lyapunov function subject to linear matrix inequalities. Secondly, the robust controllers satisfying the requirements can be designed by solving this optimization problem.Then, a new algorithm of constant thrust fitting is proposed through the impulse compensation and the fuel consumption under the theoretical continuous thrust and the actual constant thrust is calculated and compared by using the method proposed in this paper. Finally, the proposed method having the advantage of saving fuel is proved and the actual constant thrust switch control laws are obtained through the isochronous interpolation method, meanwhile, an illustrative example is provided to show the effectiveness of the proposed control design method. 一, the robust controllers satisfying the requirements can be designed by solving this optimization problem. Chen, a new algorithm of constant thrust fitting is proposed through the impulse compensation and the fuel consumption under the theoretical continuous thrust and the actual constant thrust is calculated and compared by using the method proposed in this paper . The proposed method having the advantage of saving fuel is proved and the actual constant thrust switch control laws are obtained through the isochronous interpolation method, meanwhile, an example of provided to show the effectiveness of the proposed control design method.