For the attitude control of diamond joined-wing unmanned aerial vehicle (UAV) with unknown external disturbances, the system has the characteristics of strong coupling, non-linearity, multi-input, and multi-output. Combining with sliding mode variable structure control theory, fractional calculus theory, adaptive control theory, new reaching law based on Fal function, and extended state disturbance observer, an adaptive fractional sliding mode control method was proposed. First, by introducing the fractional calculus theory and utilizing the genetic and memory characteristics of fractional calculus operators, the sliding surface of fractional calculus was designed to soften the controller output and control the overshoot of the controller. Then, in order to improve the weaknesses of traditional reaching law such as long convergence time and serious chattering, a new reaching law was proposed based on the Fal function, which could realize fast convergence without chattering. Finally, since there were modeling errors and external disturbances in the control system, the extended state observer was used to estimate and compensate the combined disturbance online. Simulation results show that the proposed control method had strong robustness and achieved ideal control effect.