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Recent experimental results provided by the CMS and LHCb, Belle and BaBarcollaborations are showing a tension with the SM predictions in $R_{K^{(*)}}$,which might call for an explanation from new physics. In this work, we examinethis tension in the type-III two-Higgs doublet models. We focus on thecontributions of charged Higgs boson to the observable(s) $R_{K^{(*)}}$ andother rare processes $\Delta M_q$ ($q=s,d$), $B \to X_s \gamma$ $B_s \to \mu^+\mu^{-}$ and $B_q \to X_s \mu^+ \mu^{-}$, which are governed by the sameeffective Hamiltonian. It is found that regions of large $\tan\beta$ and lightcharged Higgs mass $m_{H^\pm}$ can explain the measured value of $R_{K^{(*)}}$and accommodate other B physics data as well. In contrast, the type-IItwo-Higgs doublet model can not.

$R_{K^{(*)}}$ anomaly in type-III 2HDM