Previous research shows that few-cycle laser (FCL) pulses with low energy and without a bias field can be used to coherently detect terahertz (THz) pulses. As we know, it is very difficult to stabilize the carrier envelope phase (CEP) of FCL pulses, i.e., there are some random fluctuations for the CEP. Here we theoretically investigate the influence of such instability on the accuracy of THz detection. Our results show that although there is an optimum CEP for THz detection, the fluctuations of the CEP will lead to terrible thorns on the detected THz waveform. In order to solve this problem, we propose an approach using two few-cycle laser pulses with opposite CEPs, i.e., their CEPs are differed by π.