  We analyze the $B\to K_2^*(\to K\pi)l^+l^-$ (with $l=e,\mu,\tau$) decay in
the standard model and two new physics scenarios: vector-like quark model and
family non-universal $Z'$ model. We derive its differential angular
distributions, using the recently calculated form factors in the perturbative
QCD approach. Branching ratios, polarizations, forward-backward asymmetries and
transversity amplitudes are predicted, from which we find a promising
prospective to observe this channel on the future experiment. We also update
the constraints on effective Wilson coefficients and/or free parameters in
these two new physics scenarios by making use of the experimental data of $B\to
K^*l^+l^-$ and $b\to sl^+l^-$. Their impact on $B\to K_2^*l^+l^-$ is
subsequently explored and in particular the zero-crossing point for the
forward-backward asymmetry in these new physics scenarios can sizably deviate
from the SM scenario. In addition we also generalize the analysis to a similar
mode $B_s\to f_2'(1525)(\to K^+K^-) l^+l^-$.
