Nanometer grinding is the important methods of achieving the super- precision machining.The extremely thin chips can be produced by nanometer grinding. The experimental showed that the very fine chips can be down to 1 nm. Therefore molecular dynamics computer simulation can be used to analyze the mechanism of nanometer grinding.The subject which deals with the interaction between the grinding grain particles and workpiece particles was studied by the method of Gear’s predictor-corrector algorithms. The equation of motion was built up, and solved by numerical method. Then the speed and displacement of these particles were obtained.