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This paper is interested in a system of conservation laws with astiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite dif ference methods approximating this system are analyzed, which include maximum principles, bounds on the total variation, L1-bounds, and L1-continuity estimates in term of some conserved physical quantity and the characteristic variables gener ated by difference schemes with proper initial data. These estimates are necessary for the existence of a bounded-total variation (BV) solution. Furthermore, we show that numerical entropy inequalities for some convex entropy pairs of the fully system hold.Keywords:Finite difference scheme, hyperbolic conservation laws,entropy inequality