Monitoring, sensing, and exploration of over 70% of the Earth’s surface that is covered with water is permitted through the deployment of underwater bioinspired robots without affecting the natural habitat. To create a soft robot actuated with soft polymeric actuators, this paper describes the development of a lightweight jellyfish-inspired swimming robot, which achieves a maximum vertical swimming speed of 7.3 mm/s (0.05 body length/s) and is characterized by a simple design. The robot, named Jelly-Z, utilizes a contraction–expansion mechanism for swimming similar to the motion of a Moon jellyfish. The objective of this paper is to understand the behavior of soft silicone structure actuated by novel self-coiled polymer muscles in an underwater environment by varying stimuli and investigate the associated vortex for swimming like a jellyfish. To better understand the characteristics of this motion, simplified Fluid–structure simulation, and particle image velocimetry (PIV) tests were conducted to study the wake structure from the robot’s bell margin. The thrust generated by the robot was also characterized with a force sensor to ascertain the force and cost of transport (COT) at different input currents. Jelly-Z is the first robot that utilized twisted and coiled polymer fishing line (TCPFL) actuators for articulation of the bell and showed successful swimming operations. Here, a thorough investigation on swimming characteristics in an underwater setting is presented theoretically and experimentally. We found swimming metrics of the robot are comparable with other jellyfish-inspired robots that have utilized different actuation mechanisms, but the actuators used here are scalable and can be made in-house relatively easily, hence paving way for further advancements into the use of these actuators.