Brucellosis is a major problem worldwide in public health and existing work mainly focused on severity estimation based on the real data. However, global analysis on brucellosis transmission model is not well understood. In this paper, we presented a dynamical model of brucellosis transmission coupled with sheep and human populations and global analysis is shown based on Lyapunov functions. We found that the global dynamics of brucellosis model is determined by basic reproduction number R₀: if R₀ < 1, then the disease-free equilibrium is globally asymptotically stable; otherwise, the endemic equilibrium is globally asymptotically stable. We hope that our study may provide theoretical basis for the further work on brucellosis control.