In this paper, we present the LSF parameters by a unit vector form, which has directional characteristics. The underlying distribution of this unit vector variable is modeled by a von Mises-Fisher mixture model (VMM). With the high rate theory, the optimal inter-component bit allocation strategy is proposed and the distortion-rate (D-R) relation is derived for the VMM based-VQ (VVQ). Experimental results show that the VVQ outperforms our recently introduced DVQ and the conventional GVQ.