A fuzzy fractional-order PID control algorithm is investigated for target tracking of Qball-X4 quad-rotor unmanned aerial vehicle (UAV) in this paper. The gain coefficients of the proposed fractional-order PID controller are tuned based on a set of fuzzy logic rules, which can help improve the robustness of the controlled system significantly. The fractional-order membership functions which are defined by Mittag-Leffler functions and follow fat-tailed distributions are used in the fuzzy rules. Therefore, the superiority of fractional calculus is fully explored in the presented control methodology. The tracking performance of Qball-X4 UAV with the proposed fuzzy fractional-order PID controller will be much better than that controlled by the conventional PID controller.