Abstract: In an electromagnetic mesh generating system, it is important to use a good algorithm for producing reasonable and suitable mesh. In this paper,an algorithm is introduced in details, which can generate the non-uniform mesh and has been applied to "AutoMesh: An Automatically Adjustable, Non-uniform, Orthogonal FDTD Mesh Generator". These grid orthogonal coordinates and one, two and three dimensional mesh patterns, which are produced by using the algorithm, are not only accurate, but also being generated efficiently. It can be used for general mesh producing system and insure its availability and reliability.