Fracture gradient of formation is a key to determine the casing setting depth in drilling oil/gas wells. In addition, for projects, such as hydraulic fracturing and enhanced oil recovery injection, knowing the fracture gradient of the injection zone is necessary. Also, the pressure integrity of the exposed open hole dictates the maximum allowed wellbore pressure. Several theoretical and operational methods for predicting fracture pressures have been developed and refined. A Leack-off test, which is the most reliable and common method for evaluating fracture pressure gradient, is performed by too much cost and time and also this test cannot be performed at several points. In the present article, a novel technique is presented to obtain an estimation of fracture pressure gradient from drilling operation data reports. This method is based on the effect of pore pressure and confining pressure on compressive strength of rock and, consequently, on drilling speed. Artificial neural networks were implemented to build a simulator for the rate of penetration and analyze the effect of hydrostatic pressure of wellbore on the rate of penetration. The presented method was performed on field data of an Iranian southern field and the results were satisfactorily close to the actual measured fracture pressure by an average error of about 1%.