For mission requirements of space rendezvous and docking, the spacecraft relative guidance and control system is considered as a discrete-time control system. The deviation of relative motion state is predicted by using the model prediction method. Under the assumptions that thrusts are constant and limited in each control cycle, according to the influence of orbit control act on system states, the relative guidance control sequence is obtained by using the generalized inverse method. A relative guidance and control law based on spatial relative motion state transition prediction and inversion is designed. Some characteristics of this method in application are discussed. In predictive and inversive guidance control, the control output is directly expressed as orbit control acceleration, which is more in line with the actual situation of the practice. Simulation results show that the proposed method can achieve more higher accuracy, more smooth rendezvous and docking, and also has better engineering applicability in speed increment and thruster output.