The magnetization reversal processes of cobalt nanowires under different constant external magnetic fields have been studied by using the finite element micromagnetism simulation approach. The results show that magnetic domains with opposite magnetizations will be formed at one end of nanowires with a diameter of 10 nm after a nucleation time. The domain wall is classified as a transverse wall，which can be driven to move with a constant velocity by a constant external applied field from one end to the other. The velocity of domain wall is linearly dependent on the magnitude of external applied magnetic field. When H is 1000 kA/m，it is found that two head-to-head domains are found at both ends of nanowires. The calculation results show that the domain wall moves a constant distance during a period in which the direction of any magnetic moment rotates a cycle，which is independent of the magnitude of applied magnetic field.