This paper investigates dynamic hybrid beamforming (HBF) for a dual-function radar-communication (DFRC) system, where the DFRC base station (BS) simultaneously serves multiple single-antenna users and senses a target in the presence of multiple clutters. Particularly, we apply a HBF architecture with dynamic subarrays and double phase shifters in the DFRC BS. Aiming at maximizing the radar mutual information, we consider jointly designing the dynamic HBF of the DFRC system, subject to the constraints of communication quality of service (QoS), transmit power, and analog beamformer. To solve the complicated non-convex optimization, an efficient alternating optimization algorithm based on the majorization-minimization methods is developed. Simulation results verify the advancement of the considered HBF architecture and the effectiveness of the proposed design method.