The evolution of terahertz (THz) waveform in air plasma driven by low-energy few-cycle laser pulses is investigated to improve the accuracy of the carrier envelope phase (CEP) determination. Based on the transient photocurrent model, a balanced spatial distribution of the Kerr and free-electron effects in the plasma is found at 109 \mu J input energy. THz inversion occurs only once at the initial CEP of 0.5\pi, in which high-precision measurement of the CEP of few-cycle laser pulses is achieved.