The successful launching of the new generation of launch vehicle is of great practical significance to the development of China Space, and the cryogenic liquid engine commonly used in the launch vehicle has a certain probability of failures, which may affect the success or failure of rocket launching. In this paper, a Bolza problem optimization algorithm based on Radau pseudo-spectral method is proposed to solve the problem of single engine failure in the first-stage flight phase of the new generation launch vehicle by simulating fault injection and taking the attitude angle as optimal control quantity. The simulation results show that this method can effectively eliminate the influence of single engine failure on orbit injection accuracy, achieve the fault absorption of new generation launch vehicle engine, improve the fault tolerance of attitude control system, and further guarantee the system reliability.