Resin-based friction materials have been widely used in the friction braking of automobiles and power machinery. Based on experiments for the variation law of friction and wear morphology, a new model for the friction coefficient of resin-based friction materials was proposed, which includes the effects of both the micro convex body on the surface of the friction material and the frictional film generated during the friction process. This quantitative model of friction coefficient materials was established for the modelling of shear strength, compressive strength, shear strength of the frictional film, contact load and wear morphology. The shear strength, compressive strength and wear morphology of the friction material were adjusted by changing the content of basalt fibers and flaky potassium magnesium titanate. Finally, the accuracy of this quantitative model of friction coefficient was verified through experiments on friction samples with different formulations and by changing the frictional contact load. The results show that the predicted friction coefficient of the model is in good agreement with the experimental friction coefficient, the difference between the upper and lower limits of the forecast is only 5.03% and 2.30%, respectively. Meanwhile, the influence of the ratio of shear strength to compressive strength on the friction coefficient is greater than the proportion of wear morphology. The proposed friction model provides a reference value for the study of new resin-based friction materials.