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Data processing plays a crucial role in finite element analysis. Mesh generation is one of the key steps in finite element analysis. By initially using triangular meshes for preliminary generation and subsequently converting them into quadrilateral meshes through appropriate data processing, it is possible to enhancing the efficiency of mesh generation and improving computational accuracy simultaneously. In this paper, an improved approach is implemented to automatically generate multi-constrained quadrilateral finite element meshes in two-dimensional domains based on the Q-Morph algorithm. By introducing a constraint-repairing sub-algorithm, the original algorithm’s concept is adapted to accommodate these additional constraints. Additionally, the cumbersome aspects of the original algorithm’s sub-algorithms for generating the top edges of quadrilateral elements and for removing extra triangles within quadrilaterals have been adjusted. The results of example tests indicate that the constrained quadrilateral meshes generated by the proposed algorithm exhibit characteristics such as relatively uniform mesh distribution and well-organized mesh shapes.