This paper presents a mid-course trajectory optimization method for variable-flow ducted rocket (VFDR) missiles. The minimum-final time problem is defined by reflecting the dynamics and flight constraints. We represent the air mass flow rate as an analytic function of the state variables and construct an artificial neural network (ANN) for the thrust. The system equation is established by selecting the angle-of-attack and air-to-fuel ratio as control variables. Then, pseudospectral sequential convex programming (PSCP) is utilized to solve the problem. Numerical optimization results are provided to demonstrate the performance of the proposed method and examine the optimal trajectory pattern of the VFDR missiles.