Inspired by recent studies about the fluid dynamics of cephalopods in their escaping swimming mode, we propose a novel design of an underwater propulsion system using a deformable body with pressure chamber, which propels itself in burst-coast cycles through a combined effect of pulsed jet and added-mass related thrust. To investigate the performance of this system we create a freeswimming computational model-the body deformation is prescribed yet the forward motion is driven by hydrodynamic forces. Our focus is on a single bursting cycle, which corresponds to the case that the system rests between bursts. The results can also be applied to the starting stage of a continuous cruising motion. A numerical model using the boundary element method is developed to computationally study the swimming process and the dynamic characteristics of this system. The results show that in the bursting phase its peak speed depends on the size of the body, the deformation time, the amount of volume change during the deformation, and the size of the nozzle where the jet flow is generated. The optimal speed is found to coincide with the critical formation number, indicating that the formation of vortex rings in the wake plays a pivotal role in the dynamics of the system. The dynamics of the system in the coasting phase and the process of refilling the pressure chamber are also studied.