The mobility of positive and negative charge carriers has been separately measured independently of carrier concentration in low-density polyethylene (LDPE) and its nanocomposites using space charge measurements in a bilayer system. It was found that the carrier mobility of positive charge carriers was larger than that of negative charge carriers for both LDPE and its nanocomposites and that the carrier mobility was one to two orders of magnitude less in the nanocomposite than unfilled LDPE under the same conditions. The mobility is interpreted in terms of a field-assisted hopping model whose estimated activation energies were verified by measurements at different temperatures. The form of the charge traps and carrier transport is interpreted in terms of known features and electron and hole traps and the effect of nano-particles upon these features is discussed.