Here we derive the necessary and sufficient condition for the Sasakian structure corresponding to the contact metric generalized $(\kappa, \mu)$-space forms. Further, we study the contact metric generalized $(\kappa, \mu)$-space forms satisfying $B^e(\xi , X) \cdot \varphi =0,$ $B^e(\xi , X) \cdot h =0,$ and $B^e(\xi,X) \cdot S=0$, where $B^e$ is a E-Bochner curvature tensor, $h:=\frac{1}{2}\pounds _\xi \varphi$ and $S$ is the Ricci tensor.