The plague disease model that include the effect of seasonal weather variation in its transmission is investigated in this paper. The disease is caused by an extremely virulent bacteria Yersinia pestis named after a French bacteriologist Alexandre Yersin. The analysis shows that, when the periodic reproduction number (RT) is greater than one there exist a globally asymptotically stable disease free equilibrium solution (DFS). Using fundamental existence-uniqueness theorem we were able to prove the existence of positive periodic solutions. The analysis further shows that when RT > 1 then there is at least one positive periodic solution. We additionally establish the conditions for global stability of periodic solutions of the model and finally using numerical simulation we depict the behavioral dynamics of plague disease and justify the theoretical solutions.