Deceptive problems have been considered difficult for ant colony optimization (ACO) and it was believed that ACO will fail to converge to global optima of deceptive problems. This paper presents a convergence analysis of ACO on deceptive systems. This paper proves, for the first time, that ACO can achieve reachability convergence but not asymptotic convergence for a class of first order deceptive systems (FODS) without assuming a minimum pheromone at each iteration. Experimental results confirm the analysis.