With its strong endurance and high maneuverability, an underwater gliding snake-like robot (UGSR) is a strong potential candidate for aquatic exploration and monitoring. The major feature of the UGSR, which distinguishes it from other snake-like robots, is long range and long operation duration by gliding. This study establishes a gliding motion control system for the UGSR based on a sliding mode controller (SMC). The control system stabilizes the system and suppresses the uncertainties and unknown disturbances. In this strategy, chattering is reduced based on the reaching law method. To circumvent the difficulty of velocity measurements, a nonlinear observer based on an unscented Kalman filter (UKF) is employed for state estimation and random noise handling. The effectiveness of the proposed controller and observer is verified by simulating the UKF-based SMC closed-loop system.