This paper presented a generating function approach to LQ control problems with terminal constraints and the corresponding numerical methods. Different from other existing methods, the presented time-varying optimal control law does not have singularity at terminal time. The time-varying control law was constructed by solving associated Hamiltonian two-point boundary value problems via the second type generating function. Then, motivated by practical applications and computational requirements, a recursive algorithm for solving matrix differential equations of the generating function and computing optimal terminal control laws was also derived by using canonical transformation of Hamiltonian systems. As an example, a closed-loop optimal terminal controller for balanced-energy reconfiguration of formation flying satellites was designed and simulated by the proposed approaches.