In this letter, we describe a coherent subpicosecond terahertz (THz) spectroscopy system based on non-resonant optical rectification for the generation of THz radiation. We studied the two-photon absorption (TPA) of ZnTe induced by femtosecond laser pulses via THz generation, and its influence on the generation of THz radiation. Experimental results demonstrated that the intensity of pump beam against TPA must be traded off to get an optimum generation of THz radiation. As an example, we measured absorption spectrum of water vapor by time-domain spectroscopy (TDS) in the frequency range from 0.5 to 2.5 THz with a high overall accuracy.