This paper investigates trajectory optimization for aircraft evasive maneuvers against a missile using successive convex optimization, which is a relevant method to enhance the survivability of the aircraft. The evasive trajectory optimization problem incorporates the safety distance and velocity constraints to ensure that the aircraft can successfully evade the missile. We employ successive approximation to keep the nonlinearity of the missile dynamics and separate it from the original problem, which is beneficial for the rapid convergence of an iterative algorithm. Then, linearization is used to transform the remaining problem into a convex subproblem. Subsequently, a successive convex optimization algorithm is devised to compute the optimal solution of the evasive trajectory optimization problem. Numerical examples, including tail chase and head-on attack missions, demonstrate that the proposed algorithm can effectively plan the trajectories of the aircraft in various evasion scenarios.