We develop a numerical methodology to calculate quantum corrected virial coefficients using the centroid approximation of the exact path-integral expression. This approach naturally takes into account any form of the many-body non-additive interaction potentials, and - in the case of helium - is shown to have an accuracy better than 1% for temperatures larger than 100 K. We apply it to the ab initio calculation of the fourth virial coefficient of He-4, using state-of-the-art pair and three-body potentials. Our results are an improvement with respect to the classical calculation and almost agree within mutual uncertainty with the latest experimental data. (C) 2012 Elsevier B.V. All rights reserved.