Recent studies observe drilling optimization in real-time, however, among the investigated references, there is no practice working with pump pressure prediction by considering formation variables such as depth and independent parameters like Revolutions Per Minute (RPM), Hook Load. Reliable prediction of pump pressure provides an early warning of circulation problems, washout, underground blowout, and kicks helping the driller to make corrections and to safely avoid major problems. Throughout this particular study, an Artificial Neural Network model was implemented through the fitting tool of MATLAB. This model can accurately predict pump pressure versus depth in similar formations. Following the determination of the optimum model the sensitivity analysis of input parameters on the created model was investigated, an overall ranking of sensitivity degree was then provided to show the impact of each individual input parameter on this model. The simulation result was promising. Therefore, the result of this work shows the potential of a neural network approach to model the hydraulic behavior in a well. Hopefully, this work can be included in a software system which can be used in drilling planning and real-time operation of oil and gas wells in the related field that can result in decreasing Non Productive Time.