In this research, the abrasion resistance of components made by Additive Manufacturing (AM) has been modeled. AM is widely used in various industries today and the Fused Deposition Modelling (FDM) process is one of the most popular methods of fabrication in this field. Although many researches have been done with the aim of modeling mechanical behavior in this field, but limited studies have been done in the field of wear and modeling of this phenomenon. In this research, in order to create an exact mathematical relationship between the input variables (layer thickness, raster angle and air gap) and the response variable (wear rate), the experimental design using the Central Composite Design (CCD) method has been done. Twenty systematic experiments were performed to determine the response and provide a proportional regression model. Using analyze of variance (ANOVA), a mathematical model corresponding to the actual process was obtained, and the validity of the proposed model was confirmed by statistical methods. The result show that the proposed model predicts the wear rate of Acrylonitrile Butadiene Styrene (ABS) parts made by FDM method with a coefficient of determination of 95.62%. The result of the experimental study and model analysis showed that the variable of air gap and the effect of its interaction with raster angle, creates the highest wear rate and also the second-order effect of layer thickness has the most negative effect on wear rate.