The coupling of ultrashort terahertz (THz) pulses into the scanning tunneling microscope (STM) technology can make this technology with high spatial-temporal resolution, so as to play a greater role in material surface imaging, performance diagnosis and testing. Based on Simmons model, the principle of THz-STM is introduced and the factors affecting the tunneling current are analyzed. The influence of THz pulse and work function of samples on the potential barrier and tunneling current are studied in detail with numerical calculations. Particularly, the relationships between THz pulse (including its duration and phase), work function of samples, and threshold of tunneling current are discussed. It is found that the tunneling current is the period function of the phase of THz pulse. There is a threshold for the coupling of the THz and DC field, which is related to the material work function. The tunneling current is the linear function of the THz field above this threshold. It will decrease with an oscillation state and then tread to stable when the duration of the THz pulse increases. This work will help understand the mechanism of THz-STM experimental setup and might offer a reference for the related experiments.