In this article,two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media.One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment.Stability analysis and second-order error estimates in spatial meshsize for both pressure and velocity in discrete L2 norms are established on non-uniform rectangular grid.Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.