We consider the evolution of two incompressible, immiscible fluids with different densities in porus media, known as the Muskat problem  which in 2D is analogous to the Hele-Shaw cell . We first establish a local well-posedness result for initial data with asymptotics at spacial infinity and infinite energy. Then for large and monotone initial data, we establish the global existence of weak solutions by exploring a new maximum principle for the first derivative of the graph function. Our work is inspired by the recent interesting results in [13, 14, 15]. As far as we know, this is the first global large solution for a class of relatively general class of large data.