This paper reports successful development of an exact and an efficient radial basis function network (RBFN) model to estimate the head of gaseous petroleum fluids (GPFs) in electrical submersible pumps (ESPs). Head of GPFs in ESPs is now often estimated using empirical models. Overfitting and its consequent lack of model generality data is a potentially serious issue. In addition, available data series is fairly small, including the results of 110 experiments.All these limits were considered in RBFN design process, and highly accurate RBFNs were developed and cross validated.