This study aims to design and optimize a motor-driven frog-like jumping robot leg for efficient vertical jumps and multiple consecutive horizontal jumps. We have conducted bionic research on frog legs' structure and motion characteristics and further explored their motion mechanism, providing new ideas and methods for designing and manufacturing robots with high mobility and adaptability. First, our research team designed a robot leg prototype based on the frog's body structure, optimized the robot using computer-aided design software, and selected a suitable motor-driven actuator. Secondly, the weight reduction optimization of the robot body is carried out regarding material selection and topology optimization to improve the robot's maneuverability and jump height. Finally, after manufacturing the prototype of the robot legs, the robot is experimentally verified. The results show that the robot legs can achieve efficient vertical jumps (the maximum height is 1.40 meters, about 7.8 times the length of the leg link). It can also jump multiple times consecutively, which is significant for applying robots in dangerous environments, search and rescue, and other fields.