With the development of on-orbit missions, solid propulsion technology is applied to the rapid orbital maneuver of satellites. During solid propulsion maneuver, the position change of the mass center caused by the fuel consumption and the installation error of thruster have brought serious attitude disturbances. For this problem, a novel prescribed time attitude control method is proposed in this paper. Firstly, a dynamics model of the solid propulsion micro-satellite is established, while the thrust direction is adjusted by the thrust vector control (TVC) nozzle. Then, a constraint boundary function is constructed to characterize the strict fixation of the thruster operating time and an adaptive fuzzy observer is developed to quickly estimate the lumped model uncertainties. Using the backstepping method, a novel prescribed time attitude control strategy regardless of initial conditions is designed. Simulation results show that the designed controller can achieve the prescribed time convergence of satellite attitude during solid propulsion orbital maneuver, effectively.