This paper addresses the modeling and controller design of a swashplate-less coaxial helicopter with a center-of-gravity variation mechanism. The moving-mass system is used to decouple the control moments from the propulsion system. The mathematical model is thoroughly derived to capture the interaction between the dynamics of the vehicle and of the moving-mass mechanism. Furthermore, based on this model, the nonlinear controller that guarantees the exponential tracking between the system and any arbitrary trajectory is developed. This controller is designed using the geometric approach, which allows the system to be considered separately as a few subsystems. The coupling effects between these subsystems are shown to be bounded, which preserve the stability of the overall system. Two simulation trials, in which this controller is implemented, demonstrate the stability.