Based on a theoretical model and numerical simulations, the ionization currents and subsequent terahertz (THz) emission induced by the interaction of a few-cycle laser pulses with He gas targets are studied. It is shown that owing to the large transverse current generated by field ionization with few-cycle laser pulses, strong THz emission can be generated. The change of the carrier phase of the few-cycle laser pulses leads to the variation of the ionization currents. Correspondingly, the THz emission amplitude shows the characteristic as a periodic function of the carrier phase, which is also confirmed by one-dimensional particle-in-cell simulations. For a given carrier phase, the THz emission amplitude is not proportional to the laser amplitude. It shows at least two peaks at certain laser amplitudes. When the gas density profile is not uniform, the emission amplitude has a similar dependence on laser amplitude and carrier envelope phase, but the THz pulse duration and spectrum are quite different.