  In this work, we propose that there exists a moving triangle singularity in
the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process, whose position can vary from
1.158 to 1.181 GeV in the invariant mass spectrum of $K^+K^-$. After a precise
analysis on this process, it turns out that after doing some cuts on
$m_{\pi^+\pi^-}$, experiments do have the opportunity to observe this triangle
singularity. In addition, when changing the cuts on $m_{\pi^+\pi^-}$, the
movement of the predicted triangle singularity can also be observed. Thus, we
suggest future experiments, especially Super Tau-Charm Facility (STCF), to do
an anlysis on the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process to verify our
prediction.
