  Studying the hidden-charm dipion decays of the charmoniumlike state Y(4360),
we show that there exist charged charmoniumlike structures near $D\bar{D}^*$
and $D^*\bar{D}^*$ thresholds in the $J/\psi\pi^+$, $\psi(2S)\pi^+$ and
$h_c(1P)\pi^+$ invariant mass spectra of the corresponding hidden-charm dipion
decays of Y(4360) using the {\it{Initial Single Pion Emission} mechanism}. We
suggest to do further experimental study on these predicted charged enhancement
structures, especially by BESIII, Belle, and the forthcoming BelleII.
