We establish a central limit theorem for the fluctuations of the empirical measure in the β-ensemble of dimension N at a temperature proportional to N and with confining smooth potential. The space of test functions for which the CLT holds includes C1, vanishing functions at infinity. It is obtained by the inversion of an operator which is a pertubation of a Sturm-Liouville operator. The method that we use is based on a change of variables introduced by Bekerman, Guionnet and Figalli in arXiv:1311.2315 and by Shcherbina in arXiv:1310.7835.