Abstract When a spin-polarized current ‡ows through a ferromagnet, the local magnetization receives a spin transfer torque. In one-dimention approxi- mations, we solve the Landau-Lifshitz-Gilbert equation along with two spin torque terms, both analytically and numerically, to realize the behavior of a domain wall under the in‡uence of the spin-polarized current. As a …rst step, we focus on the system of domain wall within a perfect magnetic nanowire. Secondly, we consider the pinning case which may be caused by doping a high-Ku material into the system. By numerically solving the LLG equation, we …nd some characteristics of domain-wall motion under the spin-polarized current. In the presence of domain-wall pinning centers, we also de…ned the depinning …eld and construct a phase diagram for the domain-wall.