Chaos is a special form of motion in nonlinear dynamical system. It is the main form to explore the application of chaos in abstract chaotic system into mathematical model and to control it. With the deepening of chaotic system research, fractional order system gradually stands out from integer order system. By studying a new class of integer order chaotic systems, a fractional order 3d autonomous system is proposed. According to Lyapunov stability theory, the equilibrium points in chaotic systems are distinguished by the linear terms of the system, and it is found that the equilibrium points generated by the new fractionalorder system are unstable saddle points. For this fractionalorder system, the finitetime stability theory is adopted to design the synchronization controller in the drive system and response system, and the finitetime synchronization relation graph is drawn through numerical simulation to verify the realization of chaotic synchronization control in a short time.