In this work, a fractional-order (FO) sliding-mode control (SMC) scheme is developed for the trajectory-tracking problem of a quadrotor under unknown disturbances. In order to increase degree of freedom of the SM controller and enhance the convergence speed of the attitude/position state variables, a fractional-order PD switching surface is designed using fractional theory. Moreover, the upper bound of the quadrotor uncertainties and disturbances is addressed using only the velocity and position of the tracking errors. Based on Lyapunov theory, the stability of the complete system of the quadrotor is ensured. Simulation results under disturbances are done to show the effectiveness of the control method proposed in this work.