Moiré fringe expressions in many cases are analyzed and verified via simulation based on the shadow shading and spectrum analysis principles. The influence laws of the center distance of two gratings and the number of the intersection points for bright fringes on the patterns of the families of hyperbolic and elliptic moiré fringes are obtained. The research results show that the family of hyperbolic moiré fringes has more advantages on discrimination and measurement than that of elliptic moiré fringes. Based on the transmittance function of concentric-circle gratings and the computer-generated hologram, the moiré fringes of this concentric-circle grating can be generated by the use of spatial light modulator. With magnification and the suitable low-pass filter, the hyperbolic moiré fringes widely used in engineering are obtained.