The effects of Si impurity on electronic structures and magnetism of bcc Fe are investigated by using a first-principles method by considering spin-orbit coupling. In order to describe the Si impurity, a 27 atomic bcc Fe supercell has been considered. The Kohn-Sham equation was solved in terms of the all-electron full-potential linearized augmented plane wave (FLAPW) method within the generalized gradient approximation (GGA). The effects of spin-orbit coupling were calculated self-consistently by considering spin-diagonal terms based on second variation method. For the ferromagnetic (FM) state without considering SOC, the spin magnetic moment of the Si impurity was calculated to be $-0.143{mu}B$, while the magnetic moments of Fe atoms were calculated to be $2.214{mu}B$, $2.327{mu}B$, and $2.354{mu}B$ in away from the Si atom, respectively. However, the FM state with considering SOC, the spin magnetic moment of the Si impurity was calculated to be $-0.144{mu}B$, which is not affected significantly by SOC, but the spin magnetic moments of Fe atoms were calculated $2.189{mu}B$, $2.310{mu}B$, and $2.325{mu}B$, respectively, which are much reduced value compared to those of the FM state without SOC. Comparing the total charge density and spin density, those features are thought to be originated by the screening distortions of the Fe $t_{2g}$ orbital, which can be obtained by considering SOC.