During the process of the space manipulator performing on-orbit service operation tasks， a large number of operation points and complex logical constraints exist. They are affected by the redundancy of degrees of freedom， and the path costs between operation points are not unique. Therefore， it is very difficult to plan the optimal operation sequence. This paper proposes an operation sequence planning method for spatially redundant robotic arms based on an improved genetic algorithm. Firstly， a configuration transfer network model is established for the spatially redundant robotic arm to perform multi-point operation tasks， and the operation sequence planning is reduced to a complex traveling salesman problem. Secondly， the genetic algorithm is improved by randomly crossing variable-length segments and randomly changing the configuration to which the operation points belong. Moreover， the connectivity cost of the operation points is introduced in the fitness calculation， thereby adapting to the global optimal search of the spatially redundant robotic arm operation sequence. Finally， a simulation experiment is carried out taking the on-orbit multi-point inspection task performed by a seven-degree-of-freedom space manipulator as an example. Results show that the method can effectively optimize the operation sequence and significantly reduce the total path cost. Compared with the traditional genetic algorithm， it has higher operation efficiency and stronger optimization ability， demonstrating the feasibility of this method.