Snake-like robots with 3D locomotion ability have significant advantages of adaptive travelling in diverse complex terrain over traditional legged or wheeled mobile robots. Despite numerous developed gaits, these snake-like robots suffer from unsmooth gait transitions by changing the locomotion speed, direction, and body shape, which would potentially cause undesired movement and abnormal torque. Hence, there exists a knowledge gap for snake-like robots to achieve autonomous locomotion. To address this problem, this paper presents the smooth slithering gait transition control based on a lightweight central pattern generator (CPG) model for snake-like robots. First, based on the convergence behavior of the gradient system, a lightweight CPG model with fast computing time was designed and compared with other widely adopted CPG models. Then, by reshaping the body into a more stable geometry, the slithering gait was modified, and studied based on the proposed CPG model, including the gait transition of locomotion speed, moving direction, and body shape. In contrast to sinusoid-based method, extensive simulations and prototype experiments finally demonstrated that smooth slithering gait transition can be effectively achieved using the proposed CPG-based control method without generating undesired locomotion and abnormal torque.