A parameterized mesh generation and refinement method is presented for parameter sweeping analysis of electromagnetic designs. The advantages of the method are distinct in that the method is remeshing-free, thus it can significantly reduce the numerical simulation time during the finite element analysis (FEA) process. The refinement procedure is accomplished in an adaptive manner to concentrate the mesh vertices to regions with large solution variations. A high quality mesh can be obtained and kept by using this method with triangular finite elements. An example of parameter sweeping for optimal electric motor design is given to showcase the effectiveness of the proposed method.