The Q-spectral characterization of the multicone graph G ∨ K_{s }is investigated, where G is a r-regular graph of order n and K_{s} is a complete graph of order s. We prove that for any positive integer s, the multicone graph G ∨ K_{s} is determined by its Q-spectrum if r = n−2 and n ≥ 4. We also show that for any positive integer s, if r = n−3 and n ≥ 6, the multicone graph G ∨ K_{s }is determined by its Q-spectrum if and only if the complement of G has no triangles.