In this paper, an analytical calculation model of the orbital state of multiple gravity-assist trajectory is proposed. According to the model, the orbital state when arriving at the subsequent planet can be obtained from the analytical calculation of the orbital state after a GA flyby, so the state of the whole transfer can be solved. Secondly, the reachable domain of transition phase angle and the hyperbolic velocity state when the probe arrives at the subsequent planet with different departure relative velocities were explored. The extreme points in the reachable domain were extended to calculate the reachable domain at the subsequent planet. Finally, the above method is applied to design the Earth-Jupiter-Neptune transfer trajectory to the solar boundary, the influence of GA height on the phase angle reachable domain is analyzed, the corresponding relationship between phase angles and the hyperbolic velocity at the arrival of Neptune is investigated, and the transfer time distribution diagram of the final arrival at the heliosphere is determined. The above research can provide a reference for the design of the solar system marginal detection transfer orbit.