Topological insulators (TIs) have recently attracted intense theoretical and experimental interest for the existence of topologically-protected surface states in an otherwise insulating bulk. In the topological insulators, the spin-orbit coupling (SOC) plays an important role in locking the spin and momentum of electronic states. Since 5f-electrons maintain an intrinsically strong SOC, Kondo insulators will be an excellent candidate in the search of TIs. In this talk, we present our first-principles study of electronic structure and topological property of PuB4 in comparison with PuB6. We show how the SOC dramatically changes the band structure in these Pu compounds. The topological property is then analyzed by calculating the Z2 topological invariant in the Wilson loop method, and we show the surface electronic states from the calculations of the slab structure. The effects of electronic correlations are also discussed, and the results are compared against experiment.