By using a relativistic linear augmented-plane-wave method, we clarify energy band structures and Fermi surfaces of recently discovered plutonium-based superconductor PuCoGa5. We find several cylindrical sheets of Fermi surfaces with large volume, very similar to CeMIn5 (M=Ir and Co) isostructural with PuCoGa5, in spite of different f -electron numbers between Ce 3+ and Pu 3+ ions. The similarity is understood by a concept of electron-hole conversion in a tight binding model constructed based on the j-j coupling scheme. Based on the present results, we provide a possible scenario to explain why a transition temperature is so high as 18.5K in PuCoGa5. PACS numbers: 74.25.Jb, 74.70.Tx, 71.18.+y, 71.15.Rf Recently it has been discovered that PuCoGa 5 exhibits superconductivity [1]. Surprisingly its superconducting transition temperature T c is 18.5K, which is the highest among those yet observed f -electron materials and high enough even compared with other well-known intermetallic compounds. It has been also found that PuRhGa 5 becomes superconducting with T c =8.6K [2]. These plutonium intermetallic compounds PuMGa 5 have the same HoCoGa 5 -type tetragonal structure as CeMIn 5 , a family of cerium-based heavy fermion superconductors [3]. Note, however, that superconductivity occurs for M=Ir (T c =0.4K) and Co (2.3K) in CeMIn 5 , while antiferromagnetic (AFM) phase has been found for M=Rh at ambient pressure. Another isostructural material including uranium is UMGa 5 [4], but superconductivity has not been found yet. These HoCoGa 5 -type compounds are frequently referred to as "115".Regarding superconducting mechanism in the 115 compounds, first let us consider Ce-115. It has been widely considered that it is unconventional d-wave superconductor induced by AFM spin fluctuations. In fact, there are some evidences such as T 3 behavior in nuclear relaxation rate [5] and node structure measured by thermal conductivity [6]. For the phase diagram of Ce(Co,Rh,Ir)In 5 [7], AFM phase is found to exist in adjacent to the superconducting phase. Those experimental facts remind us of high-T c cuprates, but a clear difference from cuprates should be remarked. Namely, high-T c superconductivity in cuprates occurs by hole doping into AFM insulators, while in Ce-115, no hole doping is needed. To understand the appearance of superconductivity induced by AFM spin fluctuations without hole doping, a crucial role of orbital degree of freedom has been pointed out by Takimoto et al. [8].Concerning Pu-115, it is still premature to draw a definitive conclusion about the mechanism of superconductivity, but we notice that some normal-state properties in PuMGa 5 seem to be dominated by AFM spin fluctuations, e.g., the Curie-Weiss behavior in magnetic susceptibility and electric resistivity in proportion to T 1.35 [1]. Thus, it may be natural to consider that superconductivity in Pu-based compounds is also induced by AFM fluctuations. However, several problems still exist, even if d-wave superconductivity is confirmed in both Ce-115 and Pu...