  Semileptonic B meson decays induced by $b \to s(d) l^+ l^-$ flavour changing
neutral current (FCNC) transitions are very important to probe the
quark-flavour sector of the standard model (SM) and also offer a probe to test
new physics (NP). Although there exists a lot of precise results on $b \to sl^+
l^-$ induced processes, there is lack of sufficient data for $b \to dl^+ l^-$
induced decays. Here, we are interested to study $B \to \pi l^+ l^-$ and $B \to
\rho l^+ l^-$ decays which proceed via $b \to dl^+ l^-$ transition at the quark
level. In this work, we investigate the differential branching ratio,
forward-backward asymmetry, CP violation asymmetry and lepton polarization
asymmetry in these two decay channels in a non-universal Z' model. We find a
significant deviation from the SM value of these physical observables for these
decays which provide a clear conjecture for NP arising from Z' gauge boson.
