It is a big challenge for bionic legged robots to realize desired jumping heights and forward-running speeds, let alone achieve springbok-style jump-running. A key limitation is that there is no actuator system that can mimic the springbok’s muscle system to drive leg–foot system movements. In this paper, we analyze the movement process of springboks and summarize some key characteristics of actuator systems. Some key concepts are then identified based on these key characteristics. Next, we propose a new bionic hydraulic joint actuator system with impact buffering, impact energy absorption, impact energy storage, and force burst, which can be applied to various legged robots to achieve higher running speeds, higher jumping heights, longer endurance, heavier loads, and lighter mass.