Abstract: A general high-order unstructured-grid finite volume method based on least-square reconstruction and WENO limiter is presented.Some of the neighboring cells are employed to construct high-order polynomials.a least-square method is used tO solve overdetermined problem.The number of neighboring cells can be reduced with a general method,which saves memory and computing time. To achieve uniform accuracy and depress non-physical oscillation of conservation laws,a WENO limiter and rotated Riemann solver are employed.Two classical cases are provided to show resolution differences between high-order schemes and the second order scheme based on gradient reconstruction and Bath and Jesperson limiter.