The material removal rate of a quartz wafer by fixed abrasive lapping is difficult to predict； therefore， a model of the material removal rate based on contact mechanics and a generalized regression neural network （GRNN） is proposed. First， according to the ductile–brittle material removal mechanism and the simplified form of micro-contact between the abrasive block and wafer， an ideal material removal rate model was established by using calculus and the force balance principle. Then， a three-factor four-level orthogonal test was performed using the microelement method. The mapping relationship of the lapping fluid flow， lapping fluid concentration， lapping disk speed， and material removal rate correction coefficient was analyzed using the GRNN. The material removal rate model was further improved. Finally， to validate the material removal rate model， a lapping experiment was conducted. The lapping disk speed was set to 20 r/min， lapping fluid concentration to 5 wt.%， and lapping fluid flow rate to 36 ml/min. The predicted and actual values of the wafer material removal rate were simulated and measured under different lapping pressures and relative velocities. It was found that the increase in lapping pressure and relative velocity accelerates the removal of the wafer material. The predicted value of the material removal rate model exhibited the same trend as the actual value， and the error of model was 8.57%. The material removal rate model meets the demand for predicting the material removal rate of quartz wafers in fixed abrasive lapping.