The shallow water equations have important applications in hydraulic, ocean and envi-ronmental engineering. A high-resolution relaxed scheme for approximating solutions of two-dimensional shallow water equations is presented. The scheme is based on the re-laxation approximation and an improved fifth-order weighted essentially non-osscillatory (WENO) reconstruction. This reconstruction is adopted in order to improve the accu-racy and to guarantee the non-oscillatory behavior of the resulting method. A third-order strong stability preserving (SSP) Runge-Kutta scheme is used for the time discretization. The scheme benefits from the simplicity of relaxed schemes in that it avoids Riemann solvers and the computation of Jacobians. The performance of our method is illustrated by several numerical experiments. The results show that it is e?cient and robust.