The amphibious bionic robot is an unmanned system which can work both underwater and on land, which has been widely used in the fields of disaster rescue, environmental detection and resource exploration. An amphibious robot compounded with wheel and fin with the ability of self-adaptive climbing was proposed in this paper. The kinematic and dynamic mechanics of the self-adaptive climbing process was analyzed. The torque required of the critical obstacle crossing point was set as the objective function, and the optimized design structural and operational parameters were obtained by applying the genetic algorithm. Meanwhile, the climbing ability of the amphibious robot in this work was compared with others. The results illustrate that the required torque of the amphibious robot was reduced by 718.4 N·mm. The robot compounded with wheel and fin can climb the vertical obstacle of a larger height. The self-adaptive climbing process of the optimized robot was simulated. The simulation results illustrate that the variation of the propulsive velocity, the displacement and the torque in the processes of moving forward and climbing the obstacles. The experiments of the obstacle climbing was investigated for verifying the structural and operational parameters design.