In this paper, a new combination of fractional order calculus and finite time sliding mode control, used to design an aircraft autopilot. This combination aims to reduce the chattering phenomena and have a smoother control signal than conventional sliding mode. Fractional order control uses fractional integrator and derivative to improved integer order control methods. The sliding surface and sliding mode control law is proposed to reduce the chattering phenomena and also, closed-loop stability is guaranteed too. Using this algorithm, a robust autopilot against aerodynamic coefficients uncertainty is designed for an aircraft and proposed control law is utilized to stabilize the close loop system by Lyapunov stability theorem. The proposed autopilot is applied to the aircraft model and simulation results illustrate the reduction of chattering phenomena.