The IP P+M/M/c queueing system has been extensively used in the modern communication system. The existence and uniqueness of stationary distribution of the queue length L(t)for IP P+M/M/1 queue has been proved in [10]. In this paper, we shall give the suffcient and necessary conditions of l-ergodicity, geometric ergodicity, and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.