The fixed point theorems for $D^*$-metric spaces were obtained by several authors. The notion of a $D^*$-metric space and $\lambda$-generalized contractions are presented in this paper and a fixed point theorem on a $\lambda$-generalized contraction of an $f$-orbitally complete $D^*$-metric space is obtained. Further, some consequences of this fixed point theorem are presented in this paper.