This article presents a least-squares optimization model for quadrilateral mesh offsets. Starting from an initial offset mesh generated from a base quad mesh, the method improves offset quality by introducing tangential corrections at offset vertices and solving for them globally. Each correction is represented by two scalar variables associated with two independent directions taken from the corresponding base quad, so that the optimization preserves the intended offset distance while allowing the offset mesh to adjust tangentially.For each quad, the objective function is constructed from local shape-preservation terms together with a center-consistency term, so that the optimized offset quad remains as consistent as possible with the shape and size of the corresponding base quad while reducing local crimping and shearing. The resulting formulation is a global least-squares problem over the mesh and leads to a sparse linear system. Examples in both convex and concave regions show that the method can significantly improve the quality of quad-mesh offsets and can be applied iteratively for further improvement.