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Based on the mechanism of neutral meson mixing, we predict the branchingfraction of the semileptonic decay of $D_s^+\to \pi^0 \ell^+ \nu_\ell$($\ell=e$, $\mu$) using recently measured branching fraction of $D_s^+\to \etae^+\nu_e$ by BESIII experiment . We also give a formula that can describe theneutral meson mixing of $\pi^0$, $\eta$, $\eta'$ and a pseudoscalar gluonium$G$ in a unified way. The predicted branching fraction of $D_s^+\to\pi^0e^+\nu_e$ decay is $\mathcal{B}(D_s^+\to\pi^0 e^+\nu_e)=(2.65\pm 0.38)\times10^{-5}$. It is important to search for the decay $D_s^+\to \pi^0 \ell^+\nu_\ell$ in experiment, in order to understand the mechanism of $\pi^0$production in $D_s^+\to\pi^0$ transition in semileptonic decay. We alsoestimate the branching fraction of $D_s^+\to \pi^0\tau^+\nu_\tau$, which is theonly kinematically allowed semi-tauonic decay mode of the charmed meson, sincethe mass value of $D_s^+$ meson is just slightly above the threshold of$\pi^0\tau^+$ generation in the semi-tauonic decay.

Semileptonic Decay of $D_s^+\to \pi^0 \ell^+ \nu_\ell$ Via Neutral Meson Mixing