The coaxial compound helicopter with lift-offset rotors has been proposed as a concept for future high-performance rotorcraft. This helicopter usually utilizes a variable-speed rotor system to improve the high-speed performance and the cruise efficiency. A flight dynamics model of this helicopter associated with rotor speed governor/engine model is used in this article to investigate the effect of the rotor speed change and to study the variable rotor speed strategy. Firstly, the power-required results at various rotor rotational speeds are calculated. This comparison indicates that choice of rotor speed can reduce the power consumption, and the rotor speed has to be reduced in high-speed flight due to the compressibility effects at the blade tip region. Furthermore, the rotor speed strategy in trim is obtained by optimizing the power required. It is demonstrated that the variable rotor speed successfully improves the performance across the flight range, but especially in the mid-speed range, where the rotor speed strategy can reduce the overall power consumption by around 15%. To investigate the impact of the rotor speed strategy on the flight dynamics properties, the trim characteristics, the bandwidth and phase delay, and eigenvalues are investigated. It is shown that the reduction of the rotor speed alters the flight dynamics characteristics as it affects the stability, damping, and control power provided by the coaxial rotor. However, the handling qualities requirements are still satisfied with different rotor speed strategies. Finally, a rotor speed strategy associated with the collective pitch is designed for maneuvering flight considering the normal load factor. Inverse simulation is used to investigate this strategy on maneuverability in the Push-up & Pull-over Mission-Task-Element (MTE). It is shown that the helicopter can achieve Level 1 ratings with this rotor speed strategy. In addition, the rotor speed strategy could further reduce the power consumption and pilot workload during the maneuver.