  Motivated by the significant experimental progress in probing semileptonic
decays $D\to P_1P_2\ell^+\nu_\ell~(\ell=\mu,e)$, we analyze the branching
ratios of the $D\to P_1P_2\ell^+\nu_\ell $ decays with the non-resonant, the
light scalar meson resonant and the vector meson resonant contributions in this
work. We obtain the hadronic amplitude relations between different decay modes
by the SU(3) flavor analysis, and then predict relevant branching ratios of the
$D\to P_1P_2\ell^+\nu_\ell$ decays by the present experimental data with $2
\sigma$ errors. Most of our predicted branching ratios are consistent with
present experimental data within $2\sigma$ error bars, and others are
consistent with the data within $3\sigma$ error bars. We find that some
branching ratios of the non-resonant decays are on the order of
$\mathcal{O}(10^{-3}-10^{-4})$, the vector meson resonant contributions are
dominant in many decays, the non-resonant, the vector meson resonant and the
scalar resonant contributions are all important in the
$D^0\to\eta\pi^-\ell^+\nu_\ell$ decays, and both the non-resonant and the
scalar resonant contributions are important in the $D^0\to
K^-K^0\ell^+\nu_\ell,\eta'\pi^-\ell^+\nu_\ell$ and $D^+\to
\overline{K}^0K^0\ell^+\nu_\ell,\pi^0\pi^0\ell^+\nu_\ell,\eta\pi^0\ell^+\nu_\ell,\eta'\pi^0\ell^+\nu_\ell$
decays. According to our predictions, many decay modes could be observed in the
experiments like BESIII, LHCb and BelleII, and some decay modes might be
measured in these experiments in near future.
