We describe a new type of differential laser Doppler velocimeter based on the use of a modified fibre optic Sagnac interferometer. A feature of the technique is that the interferometer phase is dependent, not on the target displacement, but on its velocity. Unlike other interferometers used to measure a Doppler frequency shift directly, the practical use of the Sagnac is not restricted to very high velocities. We have noted its particular value in the measurement of high frequency oscillatory velocities, where the direct response to velocity effectively discriminates against unwanted low frequency components. To optimize the sensitivity of the interferometer, we have introduced a p/2 phase bias between the two beams, using a passive technique based on control of the birefringence of the fibre loop. We describe illustrative experiments using a vibrating target, but note other designs of optical probe for use in other applications.