In this letter, we prove that the Kurosawa-Desmedt (KD) scheme [10], which belongs to the hybrid framework, is KDM-CCA secure w.r.t. an ensemble proposed by Qin et al. in [12] under the decisional Diffie-Hellman assumption. Since our proof does not rely on the random oracle model, we partially answer the question presented by Davies and Stam in [7], where they hope to achieve the KDM-CCA security for hybrid encryption scheme in the standard model (i.e. not random oracle model). Moreover, our result may also make sense in practice since KD-scheme is (almost) the most efficient CCA secure scheme.