An accurate predictive model for rate of penetration of a drilling bit is crucial for the drilling optimization procedure. Rate of penetration is a complex function, which is dependent on many factors, such as formation properties, mud properties, weight on the bit, rotary speed, mud hydraulic, and size/type. Due to difficulty of mathematical modeling of the male of penetration, it seems impossible to present a perfect predictive model for this function. Many researchers have tried to use different approaches to present a model for rate of penetration. These approaches include empirical correlations, statistical models, and artificial neural networks. The proposed models are claimed to work well as predictive tools. In this study, different approaches of prediction of rate of penetration are tested to find the most accurate model and investigate the conditions so that each model works well. A new approach is developed to predict rate of penetration by using fuzzy logic, and this model is used in comparison. The results well illustrate that when having a large amount of data, artificial neural networks work considerably better than other approaches in the prediction of rate of penetration. Moreover: it was found that the presented mathematical equations are weak predictive tools although they are simple to use.