Underwater acoustic velocity gradient sensors are combined with pressure and vector sensors, and they are adopted to measure the particle velocity and velocity gradient components by principles of mean value and finite-difference approximation. Therefore, the directivity of underwater acoustic velocity gradient sensors will be affected by the wave length of sound source and the separation distance between the pair of sensitive elements firstly. Secondly, in practical situation, there are mismatches between the sensitive elements, including amplitude mismatch and phase mismatch. The directivity of underwater acoustic velocity gradient sensors is linked to mismatches. All the factors above which affect the directivity of underwater acoustic velocity gradient sensors are verified through simulations.