In recent years, it has been found that magnetic anisotropy in antiferromagnetic layers affects strongly exchange bias in bilayers or multilayers. However, research on magnetic nanoparticles or nanostructures is lacking. Therefore at low temperature after cooling under different fields, antiferromagnetic-anisotropy dependence of exchange bias in a single nanoparticle with unconventional antiferromagnetic (core)/ferromagnetic (shell) morphology is simulated by using a modified Monte Carlo Metropolis method, which has proved an efficient method to deal with the models with the consideration of the finite anisotropies. Common (negative) exchange bias always exists at low temperature after cooling under weak fields, independent of antiferromagnetic anisotropy. For strong cooling fields, nevertheless, positive exchange bias appears only when the antiferromagnetic anisotropy is above a critical value. The numerical results are interpreted well by means of the microscopic spin configurations of nanoparticle. The systematic study on the nanoparticle with such a special morphology will illuminate a way to solve the exchange bias puzzles. [DOI: 10.1380/ejssnt.2011.67]