A new technique for solving the forward problem in electrical capacitance tomography sensor systems is introduced. The new technique is based on training a feed-forward neural network (NN) to predict capacitance data from permittivity distributions. The capacitance data used in training and testing the NN is obtained from preprocessed and filtered experimental measurements. The new technique has shown better results when compared to the commonly used linear forward projection (LFP) while maintaining fast prediction speed. The new technique has also been integrated into a modified iterative linear back projection (Landweber) reconstruction algorithm. Reconstruction results are found to be in favor of the NN forward solver when compared to the widely used Landweber reconstruction technique with LFP forward solver.