We propose a hybrid algorithm based on the ant colony optimization (ACO) meta-heuristic, in conjunction with four well-known elimination rules, to tackle the NP-hard single-machine scheduling problem to minimize the total job tardiness. The hybrid algorithm has the same running time as that of ACO.We conducted extensive computational experiments to test the performance of the hybrid algorithm and ACO. The computational results showthat the hybrid algorithm can produce optimal or near-optimal solutions quickly, and its performance compares favourably with that of ACO for handling standard instances of the problem.