In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence w n + 1 = w n − p α + β w n / γ w n + δ w n − r , where γ w n ≠ − δ w n − r for r ∈ 0 , ∞ , α , β , γ , δ ∈ 0 , ∞ , and r > p ≥ 0 . With initial values w − p , w − p + 1 , … , w − r , w − r + 1 , … , w − 1 , and w 0 are positive real numbers. Some numerical examples are given to verify our theoretical results.