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This paper considers the leader-following consensus tracking problem of fractional-order multi-agent systems (FOMASs) that contain communication time delays. By combining the iterative learning control (ILC) approach and fractional-order calculus, a distributed PD^α-type fractional-order iterative learning control (FOILC) and a distributed D^α-type FOILC algorithm are proposed, respectively. Based on graph theory and λ-norm theory, the consensus problems of the proposed algorithms are discussed, and their convergence conditions are identified. The theoretical analysis demonstrates that as the number of iterations increases, all fractional-order agents with communication time delays can realize consensus exactly on the desired output trajectory by selecting suitable gain matrices of FOILC over a finite time interval. Illustrative examples are presented, on which the performances of the proposed method are evaluated.