A multiple homotopy method is proposed to optimize the very low thrust fuel-optimal transfer trajectory under the effects of J2 perturbation. A simple problem of high thrust

energy-optimal transfers in the linear gravity without J2 perturbation is constructed as the homotopy initial problem. Three homotopic parameters are embedded in the kinetic equations

thrust magnitude and performance index

respectively

and the optimal control laws in the homotopy process are deduced according to the minimum principle. By solving the subproblems with iterative homotopic parameters

the high thrust energy-optimal transfers

low thrust energy-optimal transfers and fuel-optimal transfers are solved in turn. A numerical example about rendezvous mission of satellite and debris on sun-synchronous orbits is given to substantiate the effectiveness of the method in fuel-optimal low thrust trajectory design in the gravity with J2 perturbation. Using the proposed method

the difficulties of the highly nonlinearity of the dynamic system caused by J2 perturbation

the fuel optimal problem's discontinuous structure of Bang-Bang control and many revolution transfers can be solved.