The three-dimensional interaction potential for HeBr2 was studied using a coupled-cluster (CCSD(T)) method. In our calculations, the Stuttgart group (SDD) effective-core potentials, augmented with diffusion (sp) and polarization (3df) functions (denoted SDD+G(3df)), basis sets are employed for the bromine atoms. For the He atom, the augmented correlation-consistent aug-cc-pV5Z basis set, supplemented with a set of bond functions, is used. The potential energy surface is constructed by fitting the CCSD(T) calculated ab initio data to an analytical expression. The present ground-state potential for HeBr2 shows a double-minimum topology, with wells for both linear and T-shaped configurations. Bound-state calculations are carried out and the lowest vibrational levels are assigned to linear and T-shaped isomers. Dissociation energies and vibrationally averaged structures for both species are determined and found to be in very good agreement with the available experimental data.