Frogs dwelling in water possess an extraordinary ability for explosive power, which enables them to leap out of the water from a floating position. The energy storage and release of the hind leg tendons and muscles are crucial for their jumping in water. To emulate the bone structure of frog hind legs and their unique jumping movement behavior, this paper proposes a consecutive aquatic jumping robot (CAJR). The CAJR comprises a four-link mechanism, two bionic water-pushing flippers and a streamlined head, which stores energy through rubber bands and employs a release mechanism and a drive rope to achieve the effect of consecutive energy storage and instantaneous release. The structure of the CAJR was initially analysed statically and dynamically. Subsequently, the energy storage capacity of the CAJR was investigated, and the maximum tension of the drive rope is 63 N. Thereafter, the terrestrial jumping process was simulated by ADAMS, revealing a jumping height to 1372 mm. The trigger was optimally designed by ANSYS to analyze the maximum equivalent stress at triggering. The relationship between the velocity and static pressure of the fluid during the process of streamlined head water discharge was simulated by Fluent. The design of this frog-inspired aquatic jumping robot offers a novel approach, with broad potential for rescue or exploration in complex terrain.