Abstract: In order to solve the shallow water equations accurately, a finite volume MUSCL scheme has been developed on an unstructured mesh consisting of arbitrary triangles. This scheme is a second-order extension of the first-order finite-volume Osher scheme proposed in Ref. 1. Second-order accuracy both In time and space can be achieved by means of an explicit predictor-corrector scheme and slope-limiting within elements. Numerical flux in the direction normal to and across each side of elements is obtained by the flux-vector splitting approach (FVS). Finally, numerical results of tidal flow for the southern branch of the Yangtze estuary and of 1-D instantaneous dam-break-induced flow are presented, to illustrate the merits of this scheme in shallow-water-hydrodynamics and enable us to consider more complex applications.