Aerial manipulation and delivery using quadrotors are becoming more and more popular in recent years. However, the displacement of the center of gravity (CoG) is a common issue experienced by these applications due to various eccentric payloads carried. Conventional quadrotors with eccentric payloads are usually stabilized by robust control strategies through adjusting rotation speeds of BLDC motors, which has negative effects on stability and energy efficiency of quadrotors. In this thesis, a flying-insect-inspired quadrotor with rotatable arms is proposed. With four rotatable arms, the proposed quadrotor can automatically estimate the displacement of the CoG and drive the four arms to their optimal positions during flight. In this way, the proposed quadrotor can move its symmetric center to the CoG of the quadrotor with the eccentric payload to increase its stability and energy efficiency. The design, dynamics modeling, and control strategy of the proposed quadrotor are presented in this thesis. Both calculation and experiment results show that the proposed quadrotor with rotatable arms has better flight performance of stability and energy efficiency than the conventional quadrotor with fixed arms.