The influences of trapped charges on carrier transport in carbon nanotubes (CNTs) are studied using CNT field-effect transistors with a partial top-gate and a global back-gate. Trapped charges induced by the global back-gate voltage sweeping (+/- 20 V) promote the device from 'ON' states to near 'OFF' states at zero gate voltage. The channel conductance and field-effect mobility of the device are significantly affected by the pre-trapped charges induced by global back-gate voltage pulses. When the partial top-gate is swept, the pre-trapped charges induced by the global back-gate voltage pulses change the conduction type of the device. In contrast, the pre-trapped charges induced by the partial top-gate voltage pulses could force the device to the 'ON' or 'OFF' state during the top-gate sweeping (+/- 4 V).