This paper focuses on the design of a fuzzy fractional Proportional- Integral-Derivative (PID) controller. The controller which is based on the conventional PID controller is modified to be P1-α I1-β D1-γ with the objective to make the controller more flexible and robust to the changes in input and the parameters. In this control structure, the fuzzy logic control acts as the tuner for the parameters α, β and γ, so that the overall controller parameter can be varied and converge better to the changes in a system. The designed fuzzy fractional PID controller is applied to a validated antilock braking system model using an electronic wedge brake system as the actuator. Numerous numerical simulations and comparisons with other fractional PID/conventional PID controllers show that the fuzzy fractional PID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.