Abstract: A continuation approach in which the thrust amplitude is the continuation parameter is proposed to solve the fuel-optimal spacecraft fly-around trajectories. On the basis of the two-impulse solution, the minimum thrust amplitude that ensures the feasibility of the fly-around trajectory is obtained by replacing impulsive thrust with finite thrust and decreasing the thrust amplitude gradually. Once obtaining the minimum-thrust solution, the thrust amplitude is increased step by step and the optimal thrusting switching sequence is determined by the primer vector in each step. Consequently, the fuel-optimal trajectories with both finite thrust and impulsive thrust are obtained by continuation from the minimum-thrust fly-around trajectory solution. By continuation on all feasible thrust amplitudes, the fuel-optimal solutions with both finite thrust and impulsive thrust are solved, and the costate variables in the optimal control problem are no longer acquired randomly. Numerical examples of slow and fast fly-around trajectories show the effectiveness of the proposed continuation approach.