  The BESIII collaboration reported an observation of two charged
charmonium-like structure $Z_c^{\pm}(3900)$ and $Z_c^{\pm}(4025)$ in $e^+e^-
\to (J/\psi \pi)^{\pm} \pi^{\mp}$ and $e^+e^- \to (D^* {\bar D}^*)^{\pm}
\pi^{\mp}$ at ${\sqrt s} =4.26$ GeV recently, which could be an analogue of
$Z_b(10610)$ and $Z_b(10650)$ claimed by the Belle Collaboration. In this work,
we investigate the hidden-charmonium transitions of $Z_c^{\pm}(3900)$ and
$Z_c^{\pm}(4025)$ via intermediate $D^{(*)} {D}^{(*)}$ meson loops. Reasonable
results for the branching ratios by taking appropriate values of $\alpha$ in
this model can be obtained, which shows that the intermediate $D^{(*)}
{D}^{(*)}$ meson loops process may be a possible mechanism in these decays. Our
results are consistent with the power-counting analysis, and comparable with
the calculations in the framework of nonrelativistic effective field theory to
some extent. We expect more experimental measurements on these
hidden-charmonium decays and search for the decays of $Z_c\to D{\bar D}^*
+c.c.$ and $Z_c^\prime \to D^* {\bar D}^*$, which will help us investigate the
$Z_c^{(\prime)}$ decays deeply.
