In this paper, we discuss a robust synchronization problem for nonlinear stochastic coupling networks through Poisson processes. The asymptotical synchronizability in probability is examined via the Hamilton-Jacobi inequality (HJI) criterion. Further, in order to effectively filter external disturbances of the nonlinear stochastic coupling networks, synchronization robustness can be guaranteed by solving an HJI. In other words, by solving two HJI criteria, both the asymptotical synchronizability and the robust synchronizability in probability are guaranteed. To simplify the HJI criteria, a linear matrix inequality criterion is imposed, allowing for robust H_∞ synchronization based on the Takagi-Sugeno fuzzy model. Finally, we propose a recursive algorithm for the core coupling design by deleting the redundant Poisson couplings of the coupling networks while maintaining its asymptotical synchronizability in probability and synchronization robustness. A simulation example is provided to illustrate the core coupling design procedure and verify the robust synchronizability.