The energy bands of the trigonal layer compound PdTe2 have been calculated, using the relativistic linear muffin-tin orbitals method. The bandstructure is separated into three distinct regions with low-lying Te 5s bands, conduction bands formed by Pd 4d and Te 5p states, and high-lying bands formed by Pd 5p, Te 6s and Te 5d states. Density of states and joint density of states have been calculated from the bands determined over the appropriate irreducible zone. The Fermi surface consists of two closed sheets in band 11 and band 13, and sheets in band 12 connected to one another by tubes. The results allow an explanation of most of the de Haas-van Alphen frequencies observed previously.