Axial-vector mesons ${a}_{1}(1260)$, ${f}_{1}(1285)$, ${h}_{1}(1170)$, ${K}_{1}(1270)$, and ${K}_{1}(1400)$ can be produced in semileptonic $\ensuremath{\tau}\ensuremath{\rightarrow}AP{\ensuremath{\nu}}_{\ensuremath{\tau}}$ decays, where $P$ stands for the pseudoscalar mesons $\ensuremath{\pi}$ or $K$. We calculate the branching ratios based in a meson dominance model. The exclusive channels ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{a}_{1}(1260{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{a}_{1}(1260{)}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$, and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{1}(1170){\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$ turn out to be of order $\mathcal{O}({10}^{\ensuremath{-}3})$, the channel ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{f}_{1}(1285){\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$ of order $\mathcal{O}({10}^{\ensuremath{-}4})$, and channels ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{1}(1270{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{1}(1270{)}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{1}(1400{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$, and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{1}(1400{)}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$ of order $\mathcal{O}({10}^{\ensuremath{-}6})$. These results indicate that the branching ratios could be measured in experiments.