Knowledge graph (KG) entity typing focuses on inferring possible entity type instances, which is a significant subtask of knowledge graph completion (KGC). Existing entity typing methods usually exploit the entity representation to model the transmission between entities and their types, which cannot fully explore the fine-grained entity typing on identifying the semantic type of an entity. To address these issues, we propose Neighborhood-Attention Neural Fine-Grained Entity Typing (AttEt), which considers the neighborhood information of the entities from KGs to bridge entities and their types together. In this paper, AttEt first develops a type-specific attention mechanism to aggregate the neighborhood knowledge of the given entity with type-specific weights. These weights are beneficial to capture various characteristics for different types of the entity, and further imply the complex correlation among these fine-grained types. Then, AttEt adaptively integrates the aggregated neighbor-level representation with entity inherent embedding to calculate the matching score between the entity and its candidate type. Besides, many entities are sparse in their relations with other entities in KGs, which makes the entity typing task more challenging. To solve this problem, we present a smooth strategy on relation-sparsity entities to improve the robustness of the model. Extensive experiments on two real-world datasets (Freebase and YAGO) show that AttEt significantly outperforms state-of-the-art baselines in the [email protected] by 2.11% on Freebase and by 8.42% on YAGO, respectively.