The Hénon-Heiles equation that is nonlinear nonintegrable Hamilton system is studied by using the method of discrete variational valculation in the Birkhoffian sense. And the result from the method is compared with the result obtained by using symplectic algorithm and Runge-Kutta method, indicating that the method presented in this paper is reasonable and feasible in computing the dynamical action of the nonlinear nonintegrable Hamilton system in the Birkhoffian sense.