In order to enhance the steering stability of a four hub-motor independent-drive electric vehicle (4MIDEV) on a road with varying adhesion coefficient, for example on a joint road, this paper proposes a hierarchical steering stability control strategy adapted to the road adhesion. The upper control level of the proposed strategy realizes the integrated control of the sideslip angle and yaw rate in the direct yaw moment control (DYC), where the influences of the road adhesion and sideslip angle are both studied by the fuzzy control. The lower control level employs a weight-based optimal torque distribution algorithm in which weight factors for each motor torque are designed to accommodate different adhesion of each wheel. The proposed stability control strategy was validated in a co-simulation of the Carsim and Matlab/Simulink platforms. The results of double-lane-change maneuver simulations under different conditions indicate that the proposed strategy can effectively achieve robustness to changes in the adhesion coefficient and improve the steering stability of the 4MIDEV.