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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 theperturbative calculations and phenomenological analysis, we find that: (a) theCP-averaged branching ratio of $B^0 \to a_1^+ a_1^-$ decay in the pQCD approachis $54.7 \times 10^{-6}$, which agrees well with the current data and thepredictions given in the QCD factorization approach within errors; (b) thenumerical results for the decay rates of other five channels are found to be inthe order of $10^{-6} \sim 10^{-5}$, which could be accessed at B factories andLarge Hadron Collider(LHC) experiments; (c) other physical observables such aspolarization fractions and direct CP-violating asymmetries are alsoinvestigated with the pQCD approach in the present work and the predictions canbe confronted with the relevant experiments in the near future; (d) thedifferent 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-Bexperiments, which could shed light on the typical QCD dynamics involved inthese decay modes, as well as in $^3P_1$ meson $a_1$ and $^1P_1$ meson $b_1$.

$B \to a_1(1260) a_1(1260)$ and $b_1(1235) b_1(1235)$ decays in the perturbative QCD approach