The present model is committed to the study of MHD boundary layer flow and heat transfer past a nonlinear vertically stretching porous stretching sheet with the effects of hydrodynamic and thermal slip. The boundary value problem, consisting of boundary layer equations of motion and heat transfer, which are nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, with the aid of similarity transformation. This problem has been solved, using Runge Kutta fourth order method with shooting technique. The effects of various physical parameters, such as, stretching parameter m, magnetic parameter M, porosity parameter fw, buoyancy parameter λ, Prandtl number Pr, Eckert number Ec, hydrodynamic slip parameter γ, and thermal slip parameter δ, on flow and heat transfer characteristics, are computed and represented graphically.