  We study some rare decays of $B$ meson involving the quark level transition
$b \to q l^+l^- (q=d,s)$ in the scalar leptoquark model. We constrain the
leptoquark parameter space using the recently measured branching ratios of
$B_{s,d} \to \mu^+ \mu^-$ processes. Using such parameters, we obtain the
branching ratios, direct CP violation parameters and isospin asymmetries in $B
\to K \mu^+ \mu^-$ and $B \to \pi \mu^+ \mu^-$ processes. We also obtain the
branching ratios for some lepton flavour violating decays $B \to l_i^+ l_j^-$.
We find that the various anomalies associated with the isospin asymmetries of
$B \to K \mu^+ \mu^-$ process can be explained in the scalar leptoquark model.
