This paper presents a convex optimization-based trajectory optimization method for variable-flow ducted rocket missiles during midcourse engagement to reach the predicted intercept point (PIP). The minimum-intercept time problem is established by reflecting the dynamics and some flight constraints for ducted rocket missiles. An artificial neural network (ANN) is utilized to approximate the nonlinear relationship between several flight conditions and the performance of ducted rockets. In addition, this study, unlike previous studies, proposes selecting the air-to-fuel ratio instead of the fuel mass-flow rate as a control input. This can alter the nonlinear constraint as an equivalent linear constraint by combining it with the pseudospectral method, which is demonstrated in this paper. A convex sub-problem is established by applying successive linearization to the nonlinear dynamic constraint. An improved trust-region algorithm is utilized with the convex sub-problem to solve the original non-convex problem. Numerical optimization results are provided to demonstrate the performance of the proposed method and investigate the optimal trajectory for variable-flow ducted rocket missiles.