Using a relativistic linear augmented-plane-wave method, we clarify energy band structures and Fermi surfaces of recently discovered plutonium-based superconductor PuCoGa5 and the isostructural material NpCoGa5. For PuCoGa5, we find several cylindrical sheets of Fermi surfaces with large volume, similar to CeMIn5, while for NpCoGa5, the Fermi surfaces are found to be similar to those of UMGa5. These similarities are discussed based on the j-j coupling scheme, suggesting some hints for the superconducting mechanism in HoCoGa5-type f-electron compounds.