The resistance distance was introduced by Klein and Randić as a generalization of the classical distance. The Kirchhoff index $Kf(G)$ of a graph $G$ is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all $n$-vertex graphs with $k$ cut vertices where $1\leq k<\frac n2$.