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This paper studies the consensus control problem for a class of stochastic multi-agent systems with nonlinear dynamics based on multi-rate sampling mechanism. First, a multi-rate sampling mechanism is introduced to sample the agent’s state asynchronously and a buffer is used to synchronize the state information of different components of the agent. Then, an edge-based event-triggered transmission mechanism is proposed to transmit the information of each agent to its neighbors in a directional manner, thereby reducing the use of communication resources and the update frequency of the controller. Next, according to the designed event-triggered transmission mechanism, the corresponding control protocol is proposed to make the stochastic multi-agent system achieve mean square consensus. Since events on different edges occur independently of each other, there is no need for clock synchronization among neighbors. Finally, a numerical simulation example is given. By comparing the synchronous sampling mechanism, the asynchronous sampling mechanism and the multi-rate sampling mechanism, we show that the proposed edge-based event-triggered transmission mechanism can achieve better performance under the multi-rate sampling mechanism.