Target-oriented sentiment classification is a fine-grained task of natural language processing to analyze the sentiment polarity of the targets. To improve the performance of sentiment classification, many approaches proposed various attention mechanisms to capture the important context words of a target. However, previous approaches ignored the significant relatedness of a target's sentiment and its local context. This paper proposes a local context-aware network (LCA-Net), equipped with the local context embedding and local context prediction loss, to strengthen the model by emphasizing the sentiment information of the local context. The experimental results on three common datasets show that local context-aware network performs superior to existing approaches in extracting local context features. Besides, the local context-aware framework is easy to adapt to many models, with the potential to improve other target-level tasks.