In this paper, a stochastic minimax optimal control strategy for uncertain quasiHamiltonian systems is proposed based on stochastic averaging method, stochastic maximum principle and stochastic differential game theory. Firstly, the partially averaged It stochastic differential equations are derived using the stochastic averaging method for quasiHamiltonian systems, while the system state transits from rapid variable of velocity and displacement into the slow variable of energy. Secondly, the stochastic optimal control of Hamiltonian system with a given performance index is converted into a minimax control problem based on the stochastic differential game theory. Thirdly, forwardbackward stochastic differential equations of the system and the adjoint process were established according to stochastic maximum principle. The worst disturbances are generated by minimizing the Hamiltonian function, while maximizing the minimal Hamiltonian function results in the worstcase optimal controls. The worst disturbances and the worstcase optimal controls are then substituting into the partially averaged It equation in order to obtain the fully averaged It equation. The responses of controlled system are predicted by solving the FokkerPlanckKolmogorov (FPK) equation associated with the fully averaged It equation. Meanwhile, the control effectiveness can also be computed. Finally, the proposed stochastic optimal control of uncertain quasiHamiltonian system is applied into a twoDOF nonlinear system. The effectiveness of the minimax control strategy is validated by numerical results.