Natural Language Inference (NLI) is a vital task in natural language processing. It aims to identify the logical relationship between two sentences. Most of the existing approaches make such inference based on semantic knowledge obtained through training corpus. The adoption of background knowledge is rarely seen or limited to a few specific types. In this paper, we propose a novel Knowledge Graph-enhanced NLI (KGNLI) model to leverage the usage of background knowledge stored in knowledge graphs in the field of NLI. KGNLI model consists of three components: a semantic-relation representation module, a knowledge-relation representation module, and a label prediction module. Different from previous methods, various kinds of background knowledge can be flexibly combined in the proposed KGNLI model. Experiments on four benchmarks, SNLI, MultiNLI, SciTail, and BNLI, validate the effectiveness of our model.