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A modified Suris hierarchy is derived by discrete zero curvature equation. Bi-Hamiltonian structure of the whole hierarchy is established through the discrete trace identity. And we prove that the obtained hierarchy is Liouville integrable. Then a one-fold Darboux- Bäcklund transformation for the modified Suris system is established by means of a proper gauge transformation matrix. As application, an explicit solution is given. Finally, as a result of the N times one-fold Darboux–Bäcklund transformation, we derive N-fold Darboux–Bäcklund transformation.