A three-dimensional (3D) carbon nanotube (CNT) network computational model was developed to investigate the electrical conductivity and current flow in polymer composites with randomly dispersed CNTs. A search algorithm was developed to determine conductive paths for 3D CNT arrangements and to account for electron tunneling effects. Tunneled currents were obtained as a function of tunneling distance and matrix material. Several possible CNT conductive paths were obtained and finite-element representative volume elements (RVEs) were then used to predict current densities in different CNT arrangements. The predictions indicate that random CNT arrangements can be optimized for current transport.