A nano-displacement measurement system with duo-gratings is analyzed by using optics theory, a mathematic model for the system is established, and the characteristic of laser Moiré signals is studied through CAD simulation. To improve signal sensitivity and positioning accuracy, two methods of precision positioning are brought forward: differential Moiré positioning method and modified Moiré positioning method. A compound control system for precision positioning is set up by combining these 2 Moiré alignment methods, in which the modified Moiré alignment technique is used for coarse alignment and the differential Moiré alignment technique is used for fine alignment, and the system obtains positioning accuracy of ±10 nm in ±500 μm positioning range with shot response time.