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Three-dimensional Monte Carlo simulation is used to investigate the electrical conductivity of nanocomposites composing of conducting nanofillers and insulating polymer matrix. When nanofillers concentrations low and they are well dispersed in the insulating matrix, electron tunneling resistance between the nanofiller junctions is found to play the dominant role in electron transport. In addition to the tunneling resistance, there is also the resistance of the conducting nanotube segments. These two types of resistance form the resistor network for electron conductance. For composites with well dispersion, individual tubes are separated by polymer molecules and the resulted tunneling resistance can be several orders larger in magnitude than the resistance of individual tubes. Considering the two types of resistors are always linked in an alternating order in the resistor network, the much larger tunneling resistance plays the determinant role in the electrical resistance of nanocomposites. When the contribution of the intrinsic tube resistance is ignored, the number of resistors in conduction paths can be reduced by more than a half and as a result, the computation efficiency is significantly improved. With improved computation efficiency, three-dimensional cubic representative volume elements with high nanotube aspect ratios up to 1000 can be simulated. Simulation results are in good agreement with the critical behaviors predicted by the classical percolation theory, as well as the reported experimental measurements.