In this study, by considering a space-based, n-joint manipulator system as research object, a kinematic and a dynamic model are constructed and the system's nonholonomic property is discussed. In light of the nonholonomic property unique to space-based systems, a path planning method is introduced to ensure that when an end-effector moves to the desired position, a floating base achieves the expected pose. The trajectories of the joints are first parameterized using sinusoidal polynomial functions, and cost functions are defined by the pose deviation of the base and the positional error of the end-effector. At this stage, the path planning problem is converted into a target optimization problem, where the target is a function of the joints. We then adopt a quantum genetic algorithm (QGA) to solve this objective optimization problem to attain the optimized trajectories of the joints and then execute nonholonomic path planning. To test the proposed method, we carried out a simulation on a six-degree-of-freedom (DOF) space-based manipulator system (SBMS). The results showed that, compared to traditional genetic optimization algorithms, the QGA converges more rapidly and has a more accurate output.