The stochastic consensus problem of linear multi-input multi-output (MIMO) multi-agent systems (MASs) with communication noises and Markovian switching topologies is studied in this technical note. The agent's full state is first estimated by the state observer, and then the estimated state is exchanged with neighbor agents through a noisy communication environment. The communication topology is randomly switching and the switching law is described by a continuous-time Markovian chain. Then a consensus protocol is proposed for this MAS, and some sufficient conditions are obtained for ensuring the mean square and almost sure consensus. In addition, if the communication topology is fixed, some necessary and sufficient conditions for the mean square consensus can be obtained according to whether or not each agent in the system has parents.