A design study for the fission product (FP) target was performed to maximize the transmutation of 99Tc and 129I in the Hybrid Power Extraction Reactor (HYPER) system without causing any core safety concerns. Localized thermal flux is obtained by inserting moderators such as CaH2. Many types of target design concepts have been investigated. The concept where 99Tc is loaded as a plate type in the outermost region and 129I is loaded as NaI rods mixed with CaH2 rods in the inner region is concluded to be the most effective in terms of transmutation rate and core power peaking. The proposed FP target is estimated to have a net transmutation rate of 5.53%/effective full-power year (EFPY) and 11.41%/EFPY for 99Tc and 129I, respectively, which are much higher compared to the transmutation rates in other fast neutron systems. In addition, the support ratios of the HYPER system for 99Tc and 129I are 5.7 and 4.0, respectively, very similar to the support ratio of TRU. The maximum pin power peaking with the loading of the FP target is 1.232, which is within the acceptable range. The loading of the FP target increases the inventory of TRU and makes the core coolant void coefficient more negative but the Doppler coefficient less negative. The proposed FP target configuration causes no safety problems in terms of core neutronics.