  In this work, we study six tree-dominated $B \to a_1(1260) a_1(1260)$ and
$b_1(1235) b_1(1235)$ decays in the perturbative QCD(pQCD) approach, where
$a_1$($b_1$) is a $^3P_1$($^1P_1$) axial-vector meson. Based on the
perturbative calculations and phenomenological analysis, we find that: (a) the
CP-averaged branching ratio of $B^0 \to a_1^+ a_1^-$ decay in the pQCD approach
is $54.7 \times 10^{-6}$, which agrees well with the current data and the
predictions given in the QCD factorization approach within errors; (b) the
numerical results for the decay rates of other five channels are found to be in
the order of $10^{-6} \sim 10^{-5}$, which could be accessed at B factories and
Large Hadron Collider(LHC) experiments; (c) other physical observables such as
polarization fractions and direct CP-violating asymmetries are also
investigated with the pQCD approach in the present work and the predictions can
be confronted with the relevant experiments in the near future; (d) the
different phenomenologies shown between $B \to a_1 a_1$ and $B \to b_1 b_1$
decays are expected to be tested by the ongoing LHC and forthcoming Super-B
experiments, which could shed light on the typical QCD dynamics involved in
these decay modes, as well as in $^3P_1$ meson $a_1$ and $^1P_1$ meson $b_1$.
