To obtain more accurate result in the finite element analysis for electric machinery, it is important to have a mesh being of good quality. This paper describes a new technique of mesh generation for the finite element method. When the list of points defining the region of analysis is given, an appropriate distribution of interior points is generated first. Secondly the points are connected to from the trianlges. Finally the connectivity data are used to reposition the interior points using Laplacian smoothing and mesh relaxation technique. In this paper, a mesh searching technique of Lawson which modifies the start mesh is proposed in addition to the above three steps. This algorithm is simple and produces the meshes being of good quality with high speed in comparison with the existing one.