Underwater robotics is rapidly evolving due to the increasing demand for marine resource exploitation. Compared with rigid robots propelled by propellers, bionic robots are stealthier and more maneuverable, such as autonomous underwater vehicles (AUVs) and remotely operated vehicles (ROVs), making them widely used underwater. In order to study the motion state of the umbrella jellyfish bionic robot, the displacement of the jellyfish robot along the same direction and the surrounding fluid pressure distribution caused by the jellyfish motion under different experimental conditions are discussed in this paper. The effect of different environmental factors on driving the jellyfish robot is determined by comparing the displacements at different observation points. The results of the study show that the lower the frequency and the longer the motion period, the greater the displacement produced by the robot within the same motion period. Frequency has a significant effect on the motion state of the jellyfish robot. While the change of amplitude also affects the motion state of the jellyfish robot, the displacement of the relaxation phase of the jellyfish robot is much smaller than that of the contraction phase with a small amplitude. It can be concluded that the effect of frequency on robot displacement is greater than the effect of amplitude on robot displacement. This study qualitatively discusses the changes of the motion state of the bionic jellyfish robot in still water under the excitation of different frequencies and amplitudes, and the results can provide corresponding reference for the future application of the bionic jellyfish robot, such as resource exploration, underwater exploration, and complex environment exploration.