Ultrashort terahertz (THz) pulses coupled with the scanning tunneling microscopy possess imaging capabilities with ultra-high spatial-temporal resolution, offering promising applications in material surface imaging, property diagnosis, and testing. The operating principle of THz tunneling scanning microscopy and the factors influencing the tunneling current are analyzed based on the Simmons model. Combined with numerical calculations, the influences of THz pulse parameters and sample work function on the barrier and tunneling current are studied in detail. The results show that the tunneling current is a periodic function of the THz pulse phase. The tunneling current induced by the THz electric field and the DC bias electric field has a critical value, determined by the work function of the material. Above this critical value, the tunneling current becomes a linear function of the THz electric field. As the THz pulse width increases, the number of electrons rectified by the tunneling current decreases in an oscillatory manner and tends to be stable. These research results have a good reference value for an in-depth understanding of the microscopic physical mechanism of terahertz tunneling scanning microscopy technology and guiding related experiments.