This work is concerned with transmutation of the highly toxic radioactive Cs-135 and Cs-137, which are extremely difficult to transmute in the conventional neutron fields, together with I-129. A novel strategy of photon and neutron hybrid transmutation has been proposed for a CsI target. An optimized laser-Compton scattering (LCS) source is used to generate energetic gamma-rays, which are then directed to central CsI target for photonuclear (gamma,n) transmutation. Energetic neutrons resulting from the (gamma,n) reactions are scattered through moderator into a surrounding CsI blanket targets where they undergo (n,gamma) transmutation. In this study, design parameters such as LCS spectrum, target dimensions and configurations have been optimized to enhance the effectiveness of the hybrid transmutation method. In addition, the CsI target configuration has also been optimized to remove heat deposited in the central target. From the results, it has been concluded that the hybrid transmutation has promising applications for the radioactive waste management. (C) 2019 Elsevier Ltd. All rights reserved.