The ABC spectral radius of a graph G is the largest eigenvalue of the ABC matrix modified from the adjacency matrix of G so that the (u,v)-entry is √(d_u+d_v-2)/√d_ud_v for an edge uv, where d_w is the degree of vertex w in G. We show that the graph formed from a cycle of length n-p by attaching p pendent edges to a vertex uniquely maximizes the ABC spectral radius over all n-vertex unicyclic graphs with p pendant edges, and over all n-vertex unicyclic graphs with girth n-p, respectively.