In this paper we develop a parallel domain decomposition method for mixed finite element methods. This algorithm is based on a procedure first formulated by Glowinski and Wheeler for a two subdomain problem. This present work involves extensions of the above method to an arbitrary number of subdomains with an inner product modification and multilevel acceleration. Both Neumann and Dirichlet boundary conditions are treated. Numerical experiments performed on the Intel iPSC/860 Hypercube are presented and indicate that this approach is scalable and fairly insensitive to variation in coefficients.