In this paper, we propose a mosquito population suppression model which is composed of two sub-models switching each other. We assume that the releases of sterile mosquitoes are periodic and impulsive, only sexually active sterile mosquitoes play a role in the mosquito population suppression process, and the survival probability is density-dependent. For the release waiting period T and the release amount c , we find three thresholds denoted by T ∗ , g ∗ and c ∗ with g ∗ < c ∗ . We show that the origin is a globally or locally asymptotically stable equilibrium when c ≥ c ∗ and T ≥ T ∗ , or c ∈ ( g ∗ ,c ∗ ) and T < T ∗ . We prove that the model generates a unique globally asymptotically stable T -periodic solution when either c ∈ ( g ∗ ,c ∗ ) and T = T ∗ , or T > T ∗ for any c > g ∗ . We give numerical examples to illustrate our theoretical results and make comparisons with some known models in the literature.