The rare-earth iron oxides RFe₂O₄ (R = Y, Ho-Lu) have a rhombohedral crystal structure, consisting of an alternating stacking of triangular lattices of R, Fe and O ions. Recently, we have proposed that this system shows a new mechanism of ferroelectricity ; the ferroelectric state originates from a polar charge-ordered structure of Fe²⁺ and Fe³⁺ on a triangular lattice. In this article, a review is given on the details of this ferroelectricity, which were revealed by measurements of synchrotron X-ray diffraction and dielectric properties of one of the RFe₂O₄ oxides, LuFe₂O₄.