  The $\eta'$ meson is associated with the U(1) anomaly. In this paper, a
successful effective chiral theory of mesons has been applied to study the
anomalous decay of $\eta'\rightarrow \pi^+\pi^-\pi^{+(0)}\pi^{-(0)}$. In this
study, the contributions of triangle and box anomalies are calculated. It is
shown that the contribution of box diagrams is important in this process. We
predict branching ratios of $Br(\eta' \rightarrow \pi^+ \pi^- \pi^+ \pi^-)={1
\over 2}Br(\eta' \rightarrow \pi^+ \pi^- \pi^0 \pi^0) = (8.3 \pm 1.2) \times
10^{-5}$, which is in good agreement with BESIII measurement.
