We investigate the two-body properties of a spin-1/2 Fermi gas subject to a spin-orbit coupling induced by laser fields. When an attractive s-wave interaction between unlike spins is present, the system may form a dimer bound state. Surprisingly, in the presence of a Zeeman field along the direction of the spin-orbit coupling, the bound state obtains finite center-of-mass mechanical momentum, whereas under the same condition but in the absence of the two-body interaction, the system has zero total momentum. This unusual result can be regarded as a consequence of the broken Galilean invariance by the spin-orbit coupling. Such a finite-momentum bound state will have profound effects on the many-body properties of the system. DOI: 10.1103/PhysRevA.87.043616