For hyperbolic conservation laws, a third-order semi-discrete central-upwind scheme with less numerical dissipation is presented. The scheme is based on a third-order non-oscillatory reconstruction proposed by Liu and Tadmor. The local speed of wave propagation is also considered. An optimal third-order strong stability preserving(SSP) Runge-Kutta method is used for time integration. The resulting scheme is free of Riemann solvers and hence no characteristic decomposition is involved, so that it enjoys the advantages of central schemes. The present scheme is tested on a variety of numerical experiments in one dimension. To illustrate the improvement of the method, the results are compared with that of the original third-order semi-discrete central-upwind scheme. The numercial results demonstrate that the presented method reduce the numerical dissipation of the semi-discrete central-upwind scheme further and improve resolution of contact waves.