The quality of finite element meshes is one of the key factors that affects the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, a local to global hexahedral mesh optimization algorithm is presented. A double octahedron based geometric transformation is used to regularize a hexahedron locally, and regular hexahedral elements are obtained for all meshes. On the basis of local operations, these regular hexahedral meshes can be further stitched and optimized by iteratively minimizing a quadric energy function, which composed of two main terms. One part is the node internal force which ensures the connectivity of regular hexahedral meshes and another is the geometric constraint which keeps the shape of original model. Applications show that the proposed algorithm is stable, and the hexahedral mesh quality is highly improved.