With the development of wireless sensor networks, distributed networks have received widespread attention. According to the different ways of connecting the nodes in the distributed network can be divided into different structures, of which the diffusion type structure is the most commonly used one due to its simple, stable and reliable. In order to improve the robustness of the diffusion subband algorithm in distributed networks, the median absolute deviation (MAD) theorem is applied to the error boundary selection, and this paper proposes a diffusion subband algorithm with a robust boundary. Through simulations, it is verified that the proposed algorithm can effectively reduce the update step size in the face of outlier interference, so that the algorithm has a good convergence performance and also has good robustness to impulsive noise.