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We calculate the important next-to-leading-order (NLO) contributions to the$B \to K K^*$ decays from the vertex corrections, the quark loops, and themagnetic penguins in the perturbative QCD (pQCD) factorization approach. ThepQCD predictions for the CP-averaged branching ratios are $Br(B^+ \to K^+\bar{K}^{*0}) \approx 3.2\times 10^{-7}$, $Br(B^+ \to \bar{K}^0 {K}^{*+})\approx 2.1\times 10^{-7}$, $Br(B^0/\ov{B}^0 \to K^0\bar{K}^{*0}+\bar{K}^0K^{*0}) \approx 8.5\times 10^{-7}$, $Br(B^0/\ov{B}^0 \to K^+K^{*-} + K^-K^{*+})\approx 1.3\times 10^{-7}$, which agree well with both the experimental upperlimits and the predictions based on the QCD factorization approach.Furthermore, the CP-violating asymmetries of the considered decay modes arealso evaluated. The NLO pQCD predictions for $\acp(B^+ \to K^+\bar{K}^{*0})$and $\acp(B^+ \to K^{*+}\bar{K}^{0})$ are $\acp^{dir}(K^+\bar{K}^{*0})\approx-6.9 %$ and $\acp^{dir}(K^{*+}\bar{K}^0)\approx 6.5 %$.

NLO contributions to $B \to K K^*$ Decays in the pQCD approach