An optimization study of a single-pass transuranic (TRU) deep burn (DB) has been performed for a block-type modular helium reactor (MHR) proposed by General Atomics. A high-burnup TRU feed vector from light water reactors is considered: 50 GWd/tU burnup with 5-yr cooling. For three-dimensional equilibrium cores, the performance analysis is done by using McCARD, a continuous-energy Monte Carlo depletion code. The core optimization is performed from the viewpoints of the core configuration, fuel management, tristructural-isotropic (TRISO) fuel specification, and neutron spectrum. With regard to core configuration, two annular cores are investigated in terms of the neutron economy. A conventional radial shuffling scheme of fuel blocks is compared with an axial-only block-shuffling strategy in terms of the fuel burnup and core power distributions. The impact of the kernel size of the TRISO fuel is evaluated, and a diluted kernel, instead of a conventional concentrated kernel, is introduced to maximize the TRU burnup by reducing the self-shielding effects of the TRISO particles. A higher graphite density is also evaluated in terms of the fuel burnup. In addition, it is shown that the core power distribution can be effectively controlled by a zoning of the packing fraction of the TRISO fuels. We also have shown that a long-cycle DB-MHR core can be designed by using a two- or three-batch fuel-reloading scheme, at the expense of only a marginal decrease of the TRU discharge burnup. Finally, preliminary safety characteristics of a DB-MHR core have been investigated in terms of the temperature coefficients and effective delayed neutron fraction. It has been found that, depending on the fuel management scheme and fuel specifications, the TRU burnup in an optimized DB-MHR core can be well over 60% in a single-pass irradiation campaign.