Charge carrier mobility in thin films of composites of single wall carbon nanotubes and poly-N-vinylcarbazole in the range of nanotube concentrations below that of the percolation threshold is studied. The drift mobility of electrons is found to range between (1.2-4.5) x 10(-6) cm(2)/(V s), which is by a factor of 5 higher than that for holes. The polymer is shown to provide the electron and hole transport in composite films.