Graph convolutional networks (GCNs) are a popular approach to learn the feature embedding of graph-structured data, which has shown to be highly effective as well as efficient in performing node classification in an inductive way. However, with massive nongraph-organized data existing in application scenarios nowadays, it is critical to exploit the relationships behind the given groups of data, which makes better use of GCN and broadens the application field. In this article, we propose the f uzzy g raph s ubspace c onvolutional n etwork (FGSCN) to provide a brand-new paradigm for feature embedding and node classification with graph convolution (GC) when given an arbitrary collection of data. The FGSCN performs GC on the f uzzy s ubspace (F-space), which simultaneously learns from the underlying subspace information in the low-dimensional space as well as its neighborliness information in the high-dimensional space. In particular, we construct the fuzzy homogenous graph G on the F -space by fusing the homogenous graph of neighborliness G and homogenous graph of subspace G (defined by the affinity matrix of the low-rank representation). Here, it is proven that the GC on F-space will propagate both the local and global information through fuzzy set theory. We evaluated FGSCN on 15 unique datasets with different tasks (e.g., feature embedding, visual recognition, etc.). The experimental results showed that the proposed FGSCN has significant superiority compared with current state-of-the-art methods.