  We investigate $R_D$ and $R_{D^*}$ anomalies in a low scale left-right
symmetric model based on $SU(3)_C\times SU(2)_L\times SU(2)_R\times
U(1)_{B-L}\times Z_2$ with a simplified Higgs sector consisting of only one
bidoublet and one $SU(2)_R$ doublet. The Wilson coefficients relevant to the
transition $b\to c\tau \nu$ are derived by integrating out the charged Higgs
$H^\pm$ boson, which gives the dominant contributions. We emphasize that the
charged Higgs effects, with the complex right-handed quark mixing matrix, can
account for both $R_D$ and $R_{D^*}$ anomalies simultaneously, while adhering
to the constraints from ${\rm BR}(B^-_c \to \tau^- \bar{\nu}_\tau) $.
