In this article, a successive convexification algorithm is presented for real-time ascent trajectory replanning of a multistage launch vehicle experiencing nonfatal dynamic faults, including the faults of thrust, mass flow, and states. This problem presents a challenge for onboard real-time guidance applications due to its nonconvex constraints, such as the heat flux constraints, and the terminal orbit entry constraints, and to its nonlinearities introduced by atmospheric effects, multiphase mass-depletion dynamics, and free flight time. After proper convexification and relaxation, the general replanning strategy and algorithm of postfault multistage launch vehicle ascent trajectory replanning problems are presented, based on a compensation-based initialization method. Numerical simulations show that the presented algorithm converges reliably after only a small number of iterations, and has a good embedded performance, making it suitable for onboard real-time applications.