A helium-helium interatomic potential energy curve was determined from quantum-mechanical ab initio calculations. Very large atom-centred basis sets including a newly developed d-aug-cc-pV8Z basis set supplemented with bond functions and ab initio methods up to full CI were applied. The aug-cc-pV7Z basis set of Gdanitz (J. Chem. Phys. 113, 5145 (2000)) was modified to be more consistent with the aug-cc-pV5Z and aug-cc-pV6Z basis sets. The diagonal Born-Oppenheimer corrections as well as corrections for relativistic effects were also calculated. A new analytical representation of the interatomic potential energy was fitted to the ab initio calculated values. In a following paper this potential model will be used in the framework of quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions.