  We first present a non-resonant description to charmonium-like structure
$Y(4360)$ in the $\psi(2S)\pi^+\pi^-$ invariant mass spectrum of the $e^+e^-\to
\psi(2S)\pi^+\pi^-$ process. The $Y(4360)$ structure is depicted well by the
interference effect of the production amplitudes of $e^{+} e^{-} \to \psi(2S)
\pi^+ \pi^-$ via the intermediate charmonia $\psi(4160)/\psi(4415)$ and direct
$e^+e^-$ annihilation into $\psi(2S)\pi^+ \pi^-$. This fact shows that
$Y(4360)$ is not a genuine resonance, which naturally explains why $Y(4360)$
was only reported in its hidden-charm decay channel $\psi(2S)\pi^+\pi^-$ and
was not observed in the exclusive open-charm decay channel or $R$-value scan.
