Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by improving their access to relevant information. However, current RAG models face challenges in matching complex semantic relationships and adapting to diverse contexts. These issues arise from the reliance on simple matching strategies, such as cosine similarity, which are limited in capturing intricate non-linear interactions between queries and documents. In this paper, we propose NeuRAG, a novel approach to RAG that adapts to diverse contexts using a trainable similarity model. NeuRAG employs neural network structures to match complex semantic relationships, enhancing retrieval and generation consistency. Our experiments demonstrate that NeuRAG as a promising approach to enhance retrieval effectiveness and improve answer generation in RAG systems.