Based on dual variable principle, a symplectic algorithm for solving optimal control problem of nonlinear dynamic system was proposed. State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time. Numerical simulation shows the precision and efficiency of the proposed algorithm.