We aim to learn the functional co-response group: a group of taxa whose co-response effect (the representative characteristic of the group showing the total topological abundance of taxa) co-responds (associates well statistically) to a functional variable. Different from the state-of-the-art method, we model the soil microbial community as an ecological co-occurrence network with the taxa as nodes (weighted by their abundance) and their relationships (a combination from both spatial and functional ecological aspects) as edges (weighted by the strength of the relationships). Then, we design a method called gFlora which notably uses graph convolution over this co-occurrence network to get the co-response effect of the group, such that the network topology is also considered in the discovery process. We evaluate gFlora on two real-world soil microbiome datasets (bacteria and nematodes) and compare it with the state-of-the-art method. gFlora outperforms this on all evaluation metrics, and discovers new functional evidence for taxa which were so far under-studied. We show that the graph convolution step is crucial to taxa with relatively low abundance (thus removing the bias towards taxa with higher abundance), and the discovered bacteria of different genera are distributed in the co-occurrence network but still tightly connected among themselves, demonstrating that topologically they fill different but collaborative functional roles in the ecological community.