Terahertz air coherent detection technique is a broadband detection method， which has been widely used in the broadband terahertz technology after its demonstration in the experiment. The frequency response of this method is determined by the duration of the probe laser pulse. Thus， the different probe lasers might induce distortions of terahertz pulses during the detection process. In this paper， the distortions and the energy loss of the terahertz pulses induced by the air coherent detection technique are quantitatively investigated based on the simulations. The results show that the pulse distortions and the energy loss depend on the duration of the probe laser pulse and the central frequency of terahertz pulse to be detected. This work will help to estimate the influence of the air coherent detection technique in the broadband terahertz technology.