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Semileptonic B meson decays induced by $b \to s(d) l^+ l^-$ flavour changingneutral current (FCNC) transitions are very important to probe thequark-flavour sector of the standard model (SM) and also offer a probe to testnew 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 quarklevel. In this work, we investigate the differential branching ratio,forward-backward asymmetry, CP violation asymmetry and lepton polarizationasymmetry in these two decay channels in a non-universal Z' model. We find asignificant deviation from the SM value of these physical observables for thesedecays which provide a clear conjecture for NP arising from Z' gauge boson.

Study of semileptonic decays $B \to \pi l^+ l^-$ and $B \to \rho l^+ l^-$ in non-universal Z' model