  Within the framework of the perturbative QCD approach, we study the two-body
charmless decays $B\to K_1(1270)(K_1(1400))\pi(K)$. We find the following
results: (i) The decays $\bar B^0\to K_1(1270)^+\pi^-, K_1(1400)^+\pi^-$ are
incompatible with the present experimental data. There exists a similar
situation for the decays $\bar B^0\to a_1(1260)^+K^-, b_1(1235)^+K^-$, which
are usually considered that the nonperturbative contributions are needed to
explain the data. But the difference is that the nonperturbative contributions
seem to play opposite roles in these two groups of decays.(ii) The pure
annihilation type decays $\bar B^0\to K_1^{\pm}(1270)K^{\mp},
K_1^{\pm}(1400)K^{\mp}$ are good channels to test whether an approach can be
used to calculate correctly the strength of the penguin-annihilation
amplitudes. Their branching ratios are predicted at $10^{-7}$ order, which are
larger than the QCDF results. (iii) The dependence of the direct CP-violating
asymmetries of these decays on the mixing angle $\theta_{K_1}$ are also
considered.
