In this paper, a fractional optimal control strategy suitable for the fractional order dynamical system is extended to the classical integral dynamical system. A stochastic fractional optimal control strategy is proposed to minimize the response of the multidegreeoffreedom (MDOF) quasinonintegrable Hamiltonian systems under Gaussian white noise excitations. First, the controlled system is reduced to a partially averaged It equation for the energy process by applying the stochastic averaging method of quasinonintegrable Hamiltonian systems. The control force part in the control performance index is then formulated as the form of fractionalorder. By combining with the stochastic dynamics programming principle, the dynamical programming equation for the ergodic control of the partially averaged system is established and then solved to yield the fractional optimal control law. Finally, an example is given to illustrate the effectiveness and efficiency of the proposed control design procedure. The numerical results indicate that the stochastic fractional optimal control strategy can be suitable for the classical integral order stochastic dynamical systems. The proposed control strategy can obtain the better control effectiveness than that of the classical integralorder optimal control strategy. Furthermore, the efficiency of integralorder control strategy becomes worse remarkably as the excitation intensity increases, while the efficiency of fractional order control strategy is a bit lower than that of integralorder control strategy, but it slowly rises and then tends to stable. The proposed stochastic fractional order optimal control strategy effectively mitigates the contradiction between the control effectiveness and control efficiency.