According to field data, there are several methods to reduce the drilling cost of new wells. One of these methods is the optimization of drilling parameters to obtain the maximum available rate of penetration (ROP). There are too many parameters affecting on ROP like hole cleaning (including drillstring rotation speed (N), mud rheology, weight on bit (WOB) and floundering phenomena), bit tooth wear, formation hardness (including depth and type of formation), differential pressure (including mud weight) and etc. Therefore, developing a logical relationship among them to assist in proper ROP selection is extremely necessary and complicated though. In such a case, Artificial Neural Networks (ANNs) is proven to be helpful in recognizing complex connections between these variables. In literature, there were various applicable models to predict ROP such as Bourgoyne and Young's model, Bingham model and the modified Warren model. It is desired to calculate and predict the proper model of ROP by using the above models and then verify the validity of each by comparing with the field data. To optimize the drilling parameters, it is required that an appropriate ROP model to be selected until the acceptable results are obtained. An optimization program will optimize the drilling parameters which can be used in future works and also leads us to more accurate time estimation. The present study is optimizing the drilling parameters, predicting the proper penetration rate, estimating the drilling time of the well and eventually reducing the drilling cost for future wells.