Let k $geq$ 1 be an integer, and let G be a 2-connected graph of order n with n $geq$ max{7, 4k+1}, and the minimum degree $delta(G)$ $geq$ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{$d_G(x)$, $d_G(y)$} $geq$ $frac{n}{2}$ for each pair of nonadjacent vertices x, y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.