Fishing moratoriums are vital for fishery management, restoring fish stocks, safeguarding ecosystems, and ensuring sustainable development. In this study, we explored and studied a canonical model with a Holling type-Ⅲ functional response consisting of two sub-equations switching each other. If the length of the closed season $\overline{T}\le T^{\ast }$, the trivial steady state is globally asymptotically stable. For $\overline{T}>T^{\ast }$, we provided a complete analysis of the existence of a unique periodic solution and three exact periodic solutions. We also provided sufficient conditions for the existence of a globally asymptotically stable periodic solution. Finally, numerical examples were provided to illustrate the theoretical results.