In this brief, the almost sure exponential consensus of multi-agent systems is investigated. A consensus protocol is designed with aperiodically intermittent communication noise rather than common continuous communication noise. Based on the consensus protocol, some sufficient conditions are given. Moreover, theoretical results show that the larger the noise control gain is, the larger the convergence rate of exponential convergency becomes in an almost sure sense. Besides, when the consensus protocol with aperiodically intermittent communication noise degenerates into one with periodically intermittent communication noise or one with common continuous communication noise, two corollaries are presented respectively. Then, the main results are used to consider almost sure exponential consensus of oscillator systems, and some simulations are provided.