Abstract: Assuming that the grit shape of brazed diamond grinding wheel is octahedron and that the grits are uniformity distributed, the contact line length between the grit and the workpiece is deduced by using the kinematic trajectory model of the grit and the finite integral method. The average thickness of the un-deformed abrasive chip is calculated by the average volume method, and then the relationship between the tangential grinding force and the unit grinding force in face grinding is deduced. The mathematical model of unit grinding force is established and verified through the rail end grinding experiment.The results show that the mathematical prediction model of unit grinding force is effective and can provide theoretical support for calculating the grinding force and temperature in subsequent end grinding.