In this work,an entropy-stable scheme is presented for hyperbolic conservation laws.An exact discontinuity capturing central solver developed recently,named MOVERS(Method of Optimal Viscosity for Enhanced Resolution of Shocks)of Jaisankar and Rao(J Computat Phys 2009;228:770-798),is designed to capture steady discontinuities exactly by enforcing Rankine-Hugoniot condition directly in the discretization process.