A fiber-optic arrangement is devised to measure the velocity difference, deltav(l), down to small separation l. With two sets of optical fibers and couplers the new technique becomes capable of measuring one component of the time- and space-resolved vorticity vector omega(r, t). The technique is tested in a steady laminar flow, in which the velocity gradient (or flow vorticity) is known. The experiment verifies the working principle of the technique and demonstrates its applications. It is found that the new technique measures the velocity difference (and hence the velocity gradient when l is known) with the same high accuracy and high sampling rate as laser Doppler velocimetry does for the local velocity measurement. It is nonintrusive and capable of measuring the velocity gradient with a spatial resolution as low as ~50 mum. The successful test of the fiber-optic technique in the laminar flow with one optical channel is an important first step for the development of a two-channel fiber-optic vorticity probe, which has wide use in the general area of fluid dynamics, especially in the study of turbulent flows.