Zero-shot learning (ZSL) is an extreme case of transfer learning that aims to recognize samples (e.g., images) of unseen classes relying on a train-set covering only seen classes and a set of auxiliary knowledge (e.g., semantic descriptors). Existing methods usually resort to constructing a visual-to-semantics mapping based on features extracted from each whole sample. However, since the visual and semantic spaces are inherently independent and may exist in different manifolds, these methods may easily suffer from the domain bias problem due to the knowledge transfer from seen to unseen classes. Unlike existing works, this paper investigates the fine-grained ZSL from a novel perspective of sample-level graph. Specifically, we decompose an input into several fine-grained elements and construct a graph structure per sample to measure and utilize element-granularity relations within each sample. Taking advantage of recently developed graph neural networks (GNNs), we formulate the ZSL problem to a graph-to-semantics mapping task, which can better exploit element-semantics correlation and local sub-structural information in samples. Experimental results on the widely used benchmark datasets demonstrate that the proposed method can mitigate the domain bias problem and achieve competitive performance against other representative methods.