To gain high mobility on challenging terrains, a mobile robot based on eccentric paddle mechanism (ePaddle) with locomotion versatility has been proposed. In this paper, a paddle-aided stair-climbing motion is presented for this ePaddle-based robot. The robot can roll on the stair as a traditional wheeled vehicle and also can climb up the stair under the help of its paddles. Robot-stair interaction modes are presented and typical feasible postures of the robot in stair-climbing are discussed. Frictional requirements for the robot to hold a desired posture are evaluated by modelling statics of the robot. Analyzed results reveal that two critical scenarios in wheeled mode occur when the front-wheel is at the bottom of the riser, and when the rear-wheel is at the top of the riser, respectively. In contrast, frictional requirements of the paddle-aided stair-climbing postures confirm that the robot can climb up the stair with all feasible postures by touching the stair with the paddle, which verifies the effectiveness of the proposed paddle-aided stair-climbing.