  We investigate the $B_{d,s}^0 \to f_1 f_1$ decays in the framework of
perturbative QCD(PQCD) approach with a referenced value $\phi_{f_1} \sim
24^\circ$. Here, $f_1$ denotes the axial-vector mesons $f_1(1285)$ and
$f_1(1420)$ with mixing angle $\phi_{f_1}$ in the quark-flavor basis. The
observables such as branching ratios, direct CP violations, and polarization
fractions of the $B_s^0 \to f_1 f_1$ decays are predicted for the first time.
We find that: (i) the almost pure penguin modes $B_s^0 \to f_1 f_1$ have large
branching ratios in the order of $10^{-6} \sim 10^{-5}$ due to the
Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences
between the amplitudes of $B_s^0 \to f_n f_s$ and $B_s^0 \to f_s f_s$ with
$f_n$ and $f_s$ being the quark-flavor states of $f_1$ mesons; (ii) The
observables receive important contributions from the weak annihilation diagrams
in the PQCD approach. In particular, without the annihilation contributions,
the $B_s^0 \to f_1(1420) f_1(1420)$ branching ratio will decrease about 81% and
its longitudinal polarization fraction will reduce around 43%. And (iii) the
dependence of the $B_{d,s}^0 \to f_1 f_1$ decay rates on $\phi_{f_1}$ exhibits
some interesting line shapes, whose confirmations would be helpful to constrain
the determination of $\phi_{f_1}$ inversely. All the PQCD predictions await for
the (near) future examinations at Large Hadron Collider beauty and/or Belle-II
experiments to further understand the properties of the axial-vector mesons and
the perturbative dynamics released from the considered decay modes.
