The harmonic index of graph G is the value H(G) =∑uv∈E(G) 2 du+dv, where dx refers to the degree of x. Zhong [The harmonic index for graphs, Appl. Math. Lett. 25 (2012) 561–566] proved that H(T) ≥ 2(n−1) n for any tree T of order n. As a results of Ali, Raza and Bhatti [Some vertex-degree-based topological indices of cacti, Ars Combin. 144 (2019) 195–206], it can be shown that H(T) ≥ 2(n−1) ℓ+1 for any tree T of order n with ℓ leaves, where 3 ≤ ℓ ≤ n − 2. In this paper, we generalize this lower bound for all cactus graphs. We present a lower bound for the harmonic index of cactus graphs G in terms of the order, the number of leaves and the number of cycles, and characterize all cactus graphs achieving equality for the given bound. [ABSTRACT FROM AUTHOR]