Esnault proved that smooth Fano varieties defined over a finite field have a rational point. It is natural to ask whether we can generalize this results to singular Fano varieties or not. As joint work with Y. Gongyo and H. Tanaka, we proved that the same statement holds for klt Fano three-folds (p > 5). In this talk, we discuss the case when the Fano variety has non-klt singularities.