<p>In nature, some undulating propulsion organisms with broad pectoral fin utilize ground effect to swim near walls such as the seabed. Inspired by these organisms, the immersed boundary method was adopted to carry out a three-dimensional numerical simulation of a self-propelled wave plate in ground effect. We had taken into account the three-dimensional flow characteristics of the wavy plate from aspects such as the initial height from the ground, the undulating parameters, and the geometric features of the body. It is found that the undulating rules of travelling wave plate in ground effect need to be controlled in order to obtain better motion performance in ground effect, and the wavy plate can enhance the thrust force rather than the lift force compared with flapping propulsion. The characteristics of the wake vortex structure of the wavy plate change with the undulating amplitude. The optimal fluctuation amplitude enables the plate to achieve a relatively good propulsion speed. Compared with other amplitudes, the swimming efficiency can be increased by 66% at the optimal fluctuation amplitude. Increasing the undulating frequency does not alter the structure of the wake vortices, but it results in a uniform enhancement of the wake vorticity intensity of the plate. When the frequency increases from 1.8 to 2.6, the cruising speed increases by 48%, and the swimming efficiency improves by 30%. For the three-dimensional shape, different shape characteristics also have an impact on it. The plate with larger aspect ratio has a higher speed and a higher swimming efficiency under the same undulating parameters.</p>