In this paper, we have proved a theorem on Hausdorff summability of Fourier series which generalizes various known results. We prove that if $$int_{0}^{t};mid phi(u)mid;du~=~o(t) ~~{m as}~~ t o 0 ~~{m and}~~ lim_{n oinfty}int_{pi/n}^{eta}frac{mid phi(t)-phi(t+pi/n)mid}{t};dt~=~o(n)$$ where $0 u=0}^{n};left(egin{array}{ll}n\
uend{array}ight);(Delta^{n-
u};mu_
u);frac{sin
u t}{t}.$$

Keywords: Hausdorff summability, Fourier series, Hausdorff transformation