We carry out Monte Carlo dynamics simulations to study the current-voltage (I-V) characteristics of one-dimensional arrays of nanoscale particles coupled by tunneling with random offset charges. The present model system is found to exhibit a voltage-driven phase transition under appropriate conditions from a insulating state to a conducting state, which is characterized by a threshold behavior of I-V curves and also a scaling behavior of the current above the threshold voltage. The results agree well with recent experiments on a chain of graphitized carbon nanoparticles.