Since the recent discovery of plutonium-based superconductors such as PuCoIn 5 , systematic studies of the electronic properties for plutonium compounds are providing insight into the itinerancy-localization crossover of Pu 5f electrons. We are particularly interested in understanding the Fermi surface properties of the PuIn 3 compound, which serves as the building block for the PuCoIn 5 superconductor. Motivated by the first observation of quantum oscillation and renewed interest in the de Haas-van Alphen (dHvA) measurements on PuIn 3 , we study the Fermi surface (FS) topology and the band dispersion in both the paramagnetic and antiferromagnetic states of PuIn 3 , based on density-functional theory with a generalized gradient approximation. We compare the results with its isostructural paramagnetic compound PuSn 3 . We present the detailed Fermi surfaces of the compounds PuIn 3 and PuSn 3 , and conclude that the FS topology of an antiferromagnetic PuIn 3 agrees better with dHvA measurements. In addition, we show the magnetization of the antiferromagnetic order can alter the field-angle dependence and values of the effective mass for the dHvA orbits. Our results suggest that the accurate determination of the magnetic order orientation with respect to the crystal orientation is crucial to advance the understanding of the electronic structure of the PuIn 3 compound.