In this paper, an explicit low-storage simplifiedM-stage Runge-Kutta (SRK) scheme for high Reynolds-number incompressible flows is presented.In the SRK scheme, the Poisson equation is solved only once in the final substage of each time step. By taking advantage of the SRK scheme and the advanced hybrid MPI+MPI model, we have developed an efficient parallel solver for buoyancy-driven turbulent flow. The spatial and temporal accuracies of the solver are validated with Taylor-Green vortex flow.Both the RK and SRK schemes are implemented for the simulation of turbulent Rayleigh-Bénard convection as well as Rayleigh-Taylor flow. The results show that the SRK scheme can save approximately 20％ of the computation time.