Study of electroencenphalography (EEG) is the one of the most utilized methods in both basic brain research and clinical diagnosis of neurological disorders. Recent technological advances in computer and electronic systems have allowed the EEG to be recorded from large electrode arrays. Modeling the brain waves using a head volume conductor model provides an effective method to localize functional generators within the brain. However, the forward solutions to this model, which represent theoretical potentials in response to current sources within the volume conductor, are difficult to compute because of time-consuming numerical procedures utilized in either the boundary element method (BEM) or the finite element method (FEM). This paper presents a novel computational approach using an artificial neural network (ANN) to map two vectors of forward solutions. These two vectors correspond to different head models but with respect to the same current source. The input vector to the ANN is based on the spherical head model, which can be computed efficiently but involves large errors. The output vector from the ANN is based on the spheroidal model, which is more precise, but difficult to compute directly using the traditional means. Our experiments indicate that this ANN approach provides a remarkable improvement over the BEM and FEM methods: 1) the mean-square error of computation was only approximately 0.3% compared to the exact solution; 2) the online computation was extremely efficient, requiring only 168 floating point operations per channel to compute the forward solution, and 10.2 K-bytes of storage to represent the entire ANN. Using this approach it is possible to perform real-time EEG modeling accurately on personal computers.