Block compression is a widely used technique to compress textures in real-time graphics applications, offering a reduction in storage size. However, their storage efficiency is constrained by the fixed compression ratio, which substantially increases storage size when hundreds of high-quality textures are required. In this paper, we propose a novel block texture compression method with neural networks, Neural Texture Block Compression (NTBC). NTBC learns the mapping from uncompressed textures to block-compressed textures, which allows for significantly reduced storage costs without any change in the shaders.Our experiments show that NTBC can achieve reasonable-quality results with up to about 70% less storage footprint, preserving real-time performance with a modest computational overhead at the texture loading phase in the graphics pipeline.