In this talk, a multilevel space-time multiplicative Schwarz method is introduced for solving parabolic equations on both spatial and temporal directions. In the implementation, the proposed method is treated as preconditioner for GMRES, that is, a coupled system arising from the discretization of the parabolic equation is solved by using a multiplicative Schwarz preconditioned GMRES algorithm. We develop an optimal convergence theory to show that the convergence rate is bounded and independent of the spatial mesh sizes, the time step size, the num- ber of subdomains, the number of levels, and the window size. Some numerical results obtained on a parallel computer with thousands of processors are pre- sented to confirm the theory in terms of optimality and scalability.