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A novel computational methodology is proposed in this work to simulate the nonlinear hydro-mechanical process in saturated porous media containing crossing fractures. Specifically, the weak form of mechanical coupling and mass transfer equations is derived based on Biot’s theory and lubrication theory, respectively. The weak discontinuity for pressure field around T-shaped crack is described by a new junction enrichment function. The nonlinear hydro-mechanical coupled equations are obtained by Extended Finite Element Method (XFEM) discretization and solved by Newton-Raphson method. This proposed computational model is verified by comparing numerical results with analytical solution. The robustness of this numerical method is demonstrated by several examples. The effects of crack orientation, matrix stiffness, and confining stress on the equivalent permeability of fractured porous medium are investigated. Numerical results indicate that the interaction of cracks plays a critical role on the hydro-mechanical behavior of the saturated porous media containing crossing fractures.