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High-order accurate Weighted Essentially Non-oscillatory (WENO) Schemes have recently been developed for finite volume methods in unstructured meshes with the developing of Mesh generation method.In this paper,the finite volume method is adopted for solving Euler equation,and the weighted least squares method is used to construct a fourth-order accuracy WENO scheme.A relatively stable method to construct stencils is presented,and a mathematical model used to solve linear weights is established.In order to obtain the non-negative linear weights,the compatibility conditions is considered as equality constraints,and non-negative conditions is considered as inequality constraints.Then,we can obtain the target function by least-square adjustment theory.Therefore,the process of solving linear weights is transformed into process of solving the optimal solution.Finally,for verifying the stability and high resolution of the schemes,two typical numerical examples are given.