This paper proposes a novel trajectory optimization method for air-launched missiles. The suggested L1-Penalized Sequential Convex Programming (LPSCP) approach reduces the order of magnitude of computation time by 2, compared to the pseudospectral approach. The new approach is directly applicable to offline trajectory planning with convergence less than 0.5 second on Intel i7-6700 cpu. Furthermore, the suggested LPSCP method has the potential to be implemented onboard, which will enable autonomous real-time guidance in the future. Throughout the paper, a convex approximation method for a generic air-launched missile guidance problem is outlined. The missile model considers thrust cut-off after burn time, which is not commonly considered in the domain of sequential convex methods. After the convexification process, given optimal guidance problem is locally approximated to form subproblems in conic form, then solved iteratively using LPSCP algorithm. The proposed method is applied to series of numerical examples to demonstrate its advantages, compared to classic pseudospectral approach. The simulation results show clear evidence of effectiveness and versatility of LPSCP algorithm on optimal missile guidance problems.