This brief studies the finite-time distributed consensus problem of fractional-order multiagent systems (FOMASs) with disturbances over directed graphs (digraphs). By utilizing the finite-time Lyapunov stability theorem and distributed estimator technique, a continuous estimator-based finite-time fully distributed algorithm with a fractional power is proposed. Under the designed algorithm, all agents’ states globally converge to a common value within a finite time in a fully distributed manner. The upper bound of the finite time is given explicitly. Finally, a numerical example is provided to validate the results.