The impregnated diamond (ID) bit drilling is one of the main rotary drilling methods in hard rock drilling and it is widely used in mineral exploration, oil and gas exploration, mining, and construction industries. In this study, the quadratic polynomial model in ID bit drilling process was proposed as a function of controllable mechanical operating parameters, such as weight on bit (WOB) and revolutions per minute (RPM). Also, artificial neural networks (ANN) model for predicting the rate of penetration (ROP) was developed using datasets acquired during the drilling operation. The relationships among mechanical operating parameters (WOB and RPM) and ROP in ID bit drilling were analyzed using estimated quadratic polynomial model and trained ANN model. The results show that ROP has an exponential relationship with WOB, whereas ROP has linear relationship with RPM. Finally, the optimal regime of mechanical drilling parameters to achieve high ROP was confirmed using proposed model in combination with rock breaking principal.