Silicene nanoribbons are one-dimensional materials made of silicene with hydrogen-modified edges. This work studies the doping of element Zn into silicene nanoribbons in the presence of an external electric field. There are two configurations studied here, top-configuration, valley-configuration. By using density functional theory (DFT) and VASP software, the energy band structures and state densities of the configurations are plotted, analyzed, and discussed. The top configuration is the most stable and optimal configuration among the studied configurations. The study also shows that there are external electric field intervals that increase the formation energy of the system, there are external electric field intervals that decrease the formation energy of the system, this represents the strength of the bonds in the material under the influence of an external electric field.. Research helps guide practical applications to create new materials and adjust material properties by external electric fields.