A novel time-dependent percolation transition has been observed in sheared carbon nanotube (CNT) composites. At a fixed CNT filler loading, the electrical conductivities of CNT composites can change abruptly as much as 8 orders of magnitude as the shear processing time increases. Microstructure characterization shows that the CNTs have aligned along the shear flow direction, which leads to the dramatic increase of the percolation threshold and thereby the dramatic decreases of the electrical conductivities. Our results highlight the great importance of understanding the response of CNT dispersion states to the processing conditions.