If an aerial defense missile with a limited strapdown field-of-view (FOV) is launched with a restricted launch angle against an incoming target at high altitude, there are significant difficulties in establishing an appropriate collision course for head-on engagement. Owing to the time-varying characteristics of the initial phase with several linear and nonlinear constraints, the analytical approach is unsuitable for obtaining the optimal solution. In this paper, a mid-course trajectory for short-range head-on engagement was generated using a convex programming approach. The time-varying characteristics of mass and velocity were considered based on the thrust profile, and the maximum flight path angle was limited as an additional constraint to prevent excessive trajectory shaping. The original nonlinear optimization problem was converted into a convex optimization problem with state augmentation, linearization, and lossless convexification. For lossless convexification, a modified optimization problem with a regularization term is suggested, and it is proved based on the maximum principal of optimal control theory. The numerical results of the modified optimization problem show that the proposed approach is effective for head-on engagement, ensuring lossless convexification. Finally, the results of the convex programming approach were compared with those of state-of-the-art nonlinear programming for verification.