Current space engineering projects such as large space structure erection and spacecraft maintenance tasks require robots with space truss climbing capability. To adapt to the complex climbing environment, this paper developed a multi-branch reconfigurable robot suitable for space truss climbing by using a cellular space robot (CSR). In different climbing environments, the robot can switch between different motion modes by changing the modules’ states. Considering the kinematic modeling problem after module reconfiguration, this paper analyzes the kinematics of the CSR based on the screw theory and extends it to any multi-branch configuration. Meanwhile, for the problem that it is difficult to obtain the inverse kinematic analytical solution of the multi-branch robot climbing mode with planar continuous three-parallel joints, the kinematic analytical algorithm for different configurations is given by combining algebraic and geometric methods. Besides, a 3D truss climbing environment is built, and the kinematic characteristics of the robot joint drive force, working space, and motion energy consumption under different motion modes of the multi-branched robot are analyzed. The results indicate that the developed multi-branched robot has good 3D space truss climbing capability and provides a basis for selecting its working mode in orbit. This study can help to broaden the application field of CSRs in orbit.