The strong few-cycle laser pulse interaction with the gas plasma filament can generate strong and broadband terahertz radiation. Here， we investigate the detail of plasma current and its terahertz radiation produced by the few-cycle laser pulse interaction with the gas plasma based on the calculations. The ionization during the plasma filamentation is in the transition between the tunnel ionization and the multiphoton ionization. The results show that this scheme can generate ultra-broadband radiation from the range of terahertz to mid-infrared， and its amplitude is a periodic function of the carrier-envelope phase of the few-cycle laser pulse. The frequency of the terahertz pulse is determined by the duration of the laser pulse， the time evolution of ionization and the plasma current， rather than by the density of the plasma. This work might give a useful clue to carry out the experiment of ultra-broadband terahertz generation by the few-cycle laser pulse interaction with the gas plasma filament.