This paper proposes an algebraic method to solve nonlinear finite-horizon optimal control problems with terminal constraints by restricting a class of nonlinear functions to rational or algebraic functions. The proposed method recursively decouples the Euler-Lagrange equations into sets of algebraic equations, where each set of equations contains only the variables of the same time instance. The candidates of the optimal solution at each time instance are obtained by solving each set. This structure of the method is suitable for nonlinear model predictive control because we can obtain the initial optimal control law by only solving a set of algebraic equations at the initial time instance. Academic and practical examples are provided to illustrate the proposed methodology and to show the efficiency of the method.