This paper describes an onboard guidance strategy which can be applied to powered landing phase of reusable launch vehicle. This method addresses the non-convex dynamic problems induced by aerodynamic forces and non-constant specific impulse variations with successive convex programming (SCP). By introducing thrust acceleration as control variable, smooth thrust command is obtained. By means of treatments such as reducing the number of trust region constraints and normalizing variables, this method significantly reduces the computational cost of the algorithm and ensures its applicability to real-time onboard planning computations. Through numerical simulations, we demonstrate the convergence robustness of the algorithm under a wide range of flight time inputs. Tests conducted on the engineeringgrade flight control computer demonstrate that the algorithm exhibits low computational complexity, which can meet the requirements of onboard guidance.