We reanalyzed nonleptonic charmless two-body B decays involving tensor mesons in final state motivated by the disagreement between current experimental information and theoretical predictions obtained in ISGW2 model for some $\mathcal{B}(B \to P(V)T)$ (where $P$, $V$ and $T$ denote a pseudoscalar, a vector and a tensor meson, respectively). We have calculated branching ratios of charmless $B \to PT$ and $B\to VT$ modes, using $B \to T$ form factors obtained in the covariant light-front (CLF) approach and the full effective Hamiltonian. We have considered the $η-η^{\prime}$ two-mixing angle formalism for $B \to η^{(\prime)}T$ channels, which increases branching ratios for these processes. Our predictions obtained in the CLF approach are, in general, greater than those computed in the framework of the ISGW2 model and more favorable with the available experimental data. Specifically, our results for exclusive channels $B \to ηK_{2}^{*}(1430)$ and $B \to ϕK_{2}^{*}(1430)$ are in agreement with recent experimental information.