Based on a tight-binding approximation electronic structure model and incorporation of the dynamic evolution method of the time-dependent density matrix equation, in this study, the ultrafast photo-current generation process is theoretically investigated from the topological material Bi₂Se₃ driven by few-cycle femtosecond laser pulse. The research results demonstrate that the light current is highly sensitive to change in the carrier waveform of the electric field, exhibiting a strong dependence on the carrier envelope phase (CEP) of the laser pulse. As the driving laser intensity increases, the electron dynamics enter a strong field interaction regime, and the ultrafast current shows significantly different variations with changes in CEP, reflecting distinct optical response phenomena of topological materials on ultrafast time scales. Specifically, it is crucial that the significant CEP-dependent light current can also be generated in the direction perpendicular to the polarization direction of the driving light. Further analysis shows that this phenomenon is closely related to topological surface states and cannot be observed in bulk states of topological materials. The research results can aid in exploring the ultrafast electron motion characteristics of surface states of topological insulators and offer theoretical guidance for the future design of optical devices operating at optical frequencies.