Annular sodium-cooled fast reactor cores [600 MW(electric)] with low sodium void worth are developed for burning transuranic nuclides discharged from light water reactors. The several core design variants are developed by changing the core configuration, the core height, the fuel assembly design and type of nonfuel assemblies in the core, and their core performance parameters including safety-related reactivity coefficients are analyzed and inter-compared. The study focuses on the core neutronic parameters without going into the detailed safety and material compatibility studies. The study shows that the several cores of the annular type can be designed to have low sodium void worth, high transmutation capability, and all the negative temperature reactivity coefficients except for the positive one related to coolant expansion that can be compensated for by the reactivity coefficients by the fuel axial expansion and the fuel Doppler effects under the off-normal events, which increase temperatures. Of the cores considered, the use of a larger central control region and fuel assemblies with high coolant flow area in the core boundaries is found to be the most effective and simple way to achieve low sodium void worth and high transmutation capability.