  We calculate the branching ratios and polarization fractions of the $B \to
a_1 b_1$ decays in the perturbative QCD(pQCD) approach at leading order, where
$a_1$($b_1$) stands for the axial-vector $a_1(1260)[b_1(1235)]$ state. By
combining the phenomenological analyses with the perturbative calculations, we
find the following results: (a) the large decay rates around $10^{-5}$ to
$10^{-6}$ of the $B \to a_1 b_1$ decays dominated by the longitudinal
polarization(except for the $B^+ \to b_1^+ a_1^0$ mode) are predicted and
basically consistent with those in the QCD factorization(QCDF) within errors,
which are expected to be tested by the Large Hadron Collider and Belle-II
experiments. The large $B^0 \to a_1^0 b_1^0$ branching ratio could provide
hints to help explore the mechanism of the color-suppressed decays. (b) the
rather different QCD behaviors between the $a_1$ and $b_1$ mesons result in the
destructive(constructive) contributions in the nonfactorizable spectator
diagrams with $a_1(b_1)$ emission. Therefore, an interesting pattern of the
branching ratios appears for the color-suppressed $B^0 \to a_1^0 a_1^0, a_1^0
b_1^0,$ and $b_1^0 b_1^0$ modes in the pQCD approach, $Br(B^0 \to b_1^0 b_1^0)
> Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$, which is different
from $Br(B^0 \to b_1^0 b_1^0) \sim Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to
a_1^0 a_1^0)$ in the QCDF and would be verified at future experiments. (c) the
large naive factorization breaking effects are observed in these $B \to a_1
b_1$ decays. Specifically, the large nonfactorizable spectator(weak
annihilation) amplitudes contribute to the $B^0 \to b_1^+ a_1^-(B^+ \to a_1^+
b_1^0\; {\rm and}\; B^+ \to b_1^+ a_1^0)$ mode(s), which demand confirmations
via the precise measurements.
