Humanoid robots, with their human-like structure and mobility, show great potential in rescue, exploration, industrial, and domestic applications. While significant progress has been made in basic locomotion, the achievement of highly explosive jumps remains challenging due to inefficient energy storage and delayed power release. This study proposes a bipedal jumping robot based on a hybrid linkage-cam mechanism to address these issues. A novel leg design combines an Electro-Hydrostatic Actuator (EHA), an ankle pitch motor, a spring-linkage energy storage unit, and a stroke amplification mechanism to boost instantaneous power output. A simplified seven-link leg model is developed, and both forward and inverse kinematic analyses are conducted to ensure accurate motion control. Additionally, a spring-loaded inverted pendulum (SLIP) model is constructed for jumping dynamics simulation, demonstrating the robot’s strong jump performance and stability.