The coaxial compound configuration has been proposed as a concept for future high-performance rotorcraft. The co-axial rotor system does not require an anti-torque device, and a propeller provides axial thrust. A well-designed control strategy for the propeller is necessary to improve the performance and the flight dynamics characteristics. A flight dynamics model of coaxial compound helicopter is developed to analyze these influences. The performance and the flight dynamics characteristics in different propeller strategies were first investigated. The results show that there is an improvement in the performance in high-speed flight when the propeller provides more propulsive forces. It also illustrates that a reasonable allocation of the rotor and the propeller in providing thrust can further reduce the power consumption in the mid speed range. In other words, the propeller control strategy can be an effective method to improve the cruise-efficiency. The flight dynamics analysis in this paper includes trim and handling qualities. The trim results prove that the propeller strategy can affect the collective pitch, longitudinal cyclic pitch, and the pitch attitude. If the control strategy is designed only to decrease the required power, it will result in a discontinuity in the trim characteristics. Handling qualities are investigated based on the ADS-33E-PRF requirement. The result demonstrates that the bandwidth and phase delay results and eigenvalue results in various speed at different propeller strategies are all satisfied. However, some propeller control strategies lead to severe inter-axis coupling in high-speed flight. Based on these results, this paper proposes the propeller control strategy for the coaxial compound helicopter. This strategy ensures good trim characteristics and handling qualities, which satisfy the related requirements, and improves the flight range or the performance in high-speed flight.