The results of nonrelativistic, augmented-plane-wave energy-band calculations have been used to calculate the Fermi surface in body-centered cubic tungsten, neglecting spin-orbit coupling. The resulting Fermi surface is very similar to one proposed earlier by Lomer for group-VI transition metals and agrees qualitatively with the available experimental results. Spin-orbit coupling is found to have little effect on the basic Fermi-surface topology in tungsten and its consequences can be understood qualitatively in terms of a simplified tight-binding calculation. Within the energy range of the tungsten $5d$ bands, the electronic density of states contains four distinct peaks, three of which lie below the tungsten Fermi energy. Assuming a rigid-band model, the present energy-band results have been used to predict the Fermi surface in the group-V transition metals.