Wheel-legged robots have fast and stable motion characteristics on flat roads, but there are the problems of poor balance ability and low movement level in special terrains such as rough roads. In this paper, a new type of wheel-legged robot with parallel four-bar mechanism is proposed, and the linear quadratic regulator (LQR) controller and fuzzy proportion differentiation (PD) jumping controller are designed and developed to achieve stable motion so that the robot has the ability to jump over obstacles and adapt to rough terrain. The amount of energy released by the parallel four-bar linkage mechanism changes with the change of the link angle, and the height of the jump trajectory changes accordingly, which improves the robot’s ability to overcome obstacles facing vertical obstacles. Simulations and real scene tests are performed in different terrain environments to verify obstacle crossing capabilities. The simulation results show that, in the pothole terrain, the maximum height error of the two hip joint motors is 2 mm for the obstacle surmounting method of the adaptive retractable wheel-legs; in the process of single leg obstacle surmounting, the maximum height error of the hip joint motors is only 6.6 mm. The comparison of simulation data and real scene experimental results shows that the robot has better robustness in moving under complex terrains.