To solve the problem of optimal fuel orbit transfer in satellite interception, this study designs an improved particle swarm optimization-genetic algorithm (PSO-GA) and combines it with the Lambert transfer method to address the two-impulse fuel-optimal interception problem in the absence of orbital perturbations. Subsequently, the minimum fuel consumption measured by the sum of the magnitudes of the impulsive velocities is obtained. When orbital perturbations lead to interception errors, the golden section impulse method is designed, and the continuous thrust compensation method is derived when the number of impulse divisions tends to infinity. During the process of compensating for interception errors with continuous thrust, the improved PSO-GA algorithm is also used to calculate the minimum fuel consumption in this process, which is represented by the total mass of the consumed fuel. The performance of the designed algorithm is evaluated by comparing it with traditional algorithms and other methods. The results show that, in terms of fuel optimization, the proposed method outperforms other methods, achieving lower fuel consumption and more efficient orbit transfer. The simulation results verify that the algorithm can effectively solve the problem of optimal fuel consumption in satellite interception, providing a practical and efficient solution for such complex scenarios.