Pyrite-structured PdSb2 with the nonsymmorphic crystalline symmetry, has long been predicted to host sixfold-degenerate exotic fermions beyond Dirac and Weyl. Although magnetotransport measurements on PdSb2 have suggested its topologically nontrivial character, the direct spectroscopic evidence still remains absent. By utilizing high-resolution angle-resolved photoemission spectroscopy, we present a systematic study on the low-energy bulk and surface electronic structure of pyrite-structured PdSb2. Through careful comparison with first-principles calculations, we verify the existence of sixfold fermions in this compound, which are formed by three doubly degenerate bands centered at the R point in the Brillouin zone. These bands exhibit parabolic dispersion close to sixfold fermion nodes, in sharp contrast to previously reported sixfold double spin-1 chiral fermions. Furthermore, our findings reveal no protected Fermi arcs in PdSb2, which is compatible with its achiral structure. Our findings suggest that pyrite-structured PdSb2 provides an ideal platform for the investigation of fermions and their potential applications.