Abstract: In this paper, an initial design method of low thrust transfer trajectories using gravity-assist based on exponential sinusoid function is introduced. Firstly, the exponential sinusoid function is established under polar coordinates to simulate the low thrust transfer trajectories. All the parameters of the transfer trajectories can be described by flight-path-angle and winding parameter. Secondly, the parameters of transfer trajectories are discretely processed with constraints, and then obtaining the intersection points of transfer trajectories with target's projected trajectories to get the polar angle to the target trajectory. The rest parameters based on exponential sinusoid can also be obtained, so that we can get the initial design parameters of low thrust transfer trajectory. Finally, the Earth-Jupiter low thrust transfer trajectory using gravity-assist by Mars is designed. The simulation results show that the method is able to search out the initial design parameters of low-thrust transfer trajectory quickly and accurately.