Single-walled carbon nanotube network field effect transistors were fabricated and studied as humidity sensors. Sensing responses were altered by changing the gate voltage. At the open channel state (negative gate voltage), humidity pulse resulted in the decrease of the source-drain current, and, vice versa, the increase in the source-drain current was observed at the positive gate voltage. This effect was explained by the electron-donating nature of water molecules. The operation speed and signal intensity was found to be dependent on the gate voltage polarity. The positive or negative change in current with humidity pulse at zero-gate voltage was found to depend on the previous state of the gate electrode (positive or negative voltage, respectively). Those characteristics were explained by the charge traps in the gate dielectric altering the effective gate voltage, which influenced the operation of field effect transistor.