A successive method is proposed in this note for the general multiple linear-quadratic control problem in discrete time. A family of auxiliary parametric linear-quadratic control problems is constructed such that its solution sequence converges to the optimal solution of the original problem. Theoretical analysis for the computational procedure and global convergence of the successive method is provided. The successive method utilizes the special structure of the problem, thus being computationally efficient and being able to furnish a closed-loop optimal control law.