A disc-type underwater glider (DTUG) has a highly symmetrical shape and is characterized by omnidirectional characteristics and high maneuverability in small bodies of water. To further explore the disc shape’s advantages and characteristics in steering motion, DTUG motion was simulated by Matlab/Simulink. Based on the structural characteristics of DTUG, the motion control equations were established. The simulation of DTUG’s steering motion is carried out and compared with a previous DTUG (LUNA). The sensitivity analysis and Lyapunov stability analysis were also conducted. The results showed that the in situ steering motion can be realized by controlling the position of the center of gravity (CG) of DTUG without moving vertically, which facilitates rapid adjustment of the yaw angle and flexible movement in small bodies of water. The in situ steering motion was significantly affected by the control parameters. The parameter that had the greatest effect on it can be obtained through sensitivity analysis, which can guide DTUG to better adjust the yaw angle under different conditions. The stability analysis showed that the DTUG can remain stable within the range of the control parameter.