Abstract In order to manufacture structured surfaces, firstly, the abrasive stone model with staggered abrasive particles is established with mathematical methods. Secondly, the motion of abrasive particles on the abrasive stone is designed. Finally, the surface morphology of the workpiece is simulated. The simulated workpiece morphology under different machining parameters is compared, and the influence of different machining parameters on the workpiece surface morphology is obtained. The results indicate that the microstructured surface can be lapped by using the abrasive stone of staggered abrasive particles. As the amplitude and frequency of the abrasive stone increase, the number of protrusions increases, and the area of individual protrusions decreases.