Most of recently developed rescue robots can only be deployed to limited attacked regions after tsunami and the floods, due to their limited mobility on complex amphibious terrains. To access such amphibious environments with improved mobility, we propose a novel eccentric paddle mechanism (ePaddle) which has a set of paddles eccentrically placed in a wheel to perform multiple terrestrial, aquatic, and amphibious gaits. One of the advantages of our proposed ePaddle mechanism is its unique locomotion versatility introduced by the eccentric distance between the paddle shaft and the wheel center. We demonstrate this versatility by proposing five typical gaits for traveling on different terrains. For instance, wheeled rolling gait is used to achieve high-speed locomotion on even terrain. Legged gait is applied to travel on the rough terrains. To access the soft terrains where wheels slip and legs sink, a wheel-leg-integrated gait is performed by digging the paddle into the ground. To swim in the water, rotational paddling and oscillating paddling gaits are proposed. For each of these gaits, standard gait sequence is defined and joint parameters are calculated based on kinematics. An ePaddle prototype is then built and tested with the proposed gait sequences. Experimental results verify the design of the ePaddle mechanism as well as its versatile gaits.