Rate of penetration (ROP) modeling is one of the most important objectives of any drilling program. Penetration model depends on different criteria such as mud weight (MW), weight on bit (WOB), rotary speed (N), and so forth. It is a complex process, because of the high number of variables and uncertainties. Different mathematical models and evaluation methods were developed to solve this problem but they were unable to attain desirable accuracy. Adaptive neuro-fuzzy inference systems (ANFIS) could be used in these cases to predict the rate of penetration. ANFIS is a combination of neural networks and fuzzy logic networks and could be used to create a robust ROP model. The objective of this study is to apply the ANFIS method and compare the modeling results with conventional artificial neural network models. ANFIS trains the model using a set amount of data and then validates it against random data to measure the error. Drill bit record from a certain field has been taken as training data and testing data for the program. The selection process uses the Sugeno model for generating the fuzzy model and the backpropagation and gradient descent method for recognizing the patterns. The data was normalized and sorted out to remove the incomplete values. Tests were done by applying 2 and 3 membership functions to a 4 input interface and a 5 input interface. The accuracy of the results depends on the numbers of inputs and membership functions. Each input was tested with different membership functions to test the data. The output generated from the training process showed that sigmoid function and Gaussian function with grid partitioning and linear output function yielded the best results for 4 and 5 inputs using 2 and 3 membership functions each. The training error recorded was about 3 percent with a checking error of 20 percent for most cases.