To address the multi-constraint autonomous rendezvous problem for maneuvering non-cooperative space targets, this paper proposes a trajectory planning and control method in the Line-of-Sight (LOS) coordinate frame of the chaser spacecraft, which integrates a genetic algorithm with Linear Time-Varying Model Predictive Control (LTV-MPC). The proposed method overcomes the limitations of conventional controllers designed in the Local Vertical Local Horizontal (LVLH) frame for rendezvous missions with maneuvering non-cooperative targets, while avoiding navigation coordinate transformation errors. First, a relative motion dynamic model between the non-cooperative target and the chaser spacecraft is established in the chaser’s LOS coordinate frame. Then, taking full account of multiple constraints including dynamics, control saturation and safety constraints, an optimization model is constructed with a fuel-optimal performance index. The model is solved using a genetic algorithm, taking advantage of its global convergence and strong constraint-handling ability, to obtain the optimal nominal trajectory. Finally, benefiting from its advantages in conveniently handling multiple constraints and uncertainties, an LTV-MPC-based closed-loop tracking controller is designed to track the aforementioned nominal trajectory. Numerical simulations show that the designed trajectory satisfies complex engineering constraints including control, dynamics and safety, and is fuel-optimal, controllable and achievable. In addition, the controller exhibits favorable control accuracy and robustness in the presence of uncertainties, providing an effective solution to the rendezvous problem with maneuvering non-cooperative space targets.