In a programming operation of a 3D stacked non-volatile memory device, the channel of an inhibited NAND string is pre-charged by gate-induced drain leakage (GIDL) to achieve a high level of boosting which prevents program disturb in inhibited storage elements. In a program-verify iteration, prior to applying a program pulse, the drain-side select gate transistor is reverse biased to generate GIDL, causing the channel to be boosted to a pre-charge level such as 1.5V. Subsequently, when the program pulse is applied to a selected word line and pass voltages are applied to unselected word lines, the channel is boosted higher from the pre-charge level due to capacitive coupling. The pre-charge is effective even for a NAND string that is partially programmed because it does not rely on directly driving the channel from the bit line end.