This paper studies the leaderless consensus of the stochastic multi-agent systems based on partial differential equations–ordinary differential equations (PDE-ODEs). Compared with the traditional state coupling, the most significant difference between this paper is that the space state coupling is designed. Two boundary couplings are investigated in this article, respectively, collocated boundary measurement and distributed boundary measurement. Using the Lyapunov directed method, sufficient conditions for the stochastic multi-agent system to achieve consensus can be obtained. Finally, two simulation examples show the feasibility of the proposed spatial boundary couplings.