Brain magnetic resonance imaging (MRI) is crucial for diagnosing and understanding neurological disorders, but inherent limitations hinder the visualization of fine details in brain structures. The emergence of super‐resolution techniques, especially deep‐learning methods, has improved imaging quality of MRI, by increasing MRI spatial resolution. At present, deep‐learning algorithms mostly performed super‐resolution on 2D MRI images. However, considering 3D nature of MRI, 3D models are more suitable for brain MRI super‐resolution. To achieve finer brain structural details, this study proposes a 3D brain MRI super‐resolution method based on diffusion model (3D‐SRDM), which is a fast and easily trainable neural network for the generation of high‐resolution brain MRI images. In our 3D‐SRDM model, the self‐attention module in U‐Net is replaced with 3D spatial attention mechanism. The network structure of 3D‐SRDM is optimized to reduce training parameters. Moreover, accelerated sampling from denoising diffusion implicit model is also incorporated to reduce time consumption. By these optimizations, compared with original diffusion model, the proposed model can achieve about 10‐ and 5‐fold speed increase at 4× and 8× super‐resolution of 3D brain MRI volumes, respectively, almost without affecting image quality. Thus, 3D‐SRDM has potential application value in efficiently generating high‐resolution 3D brain MRI images, thus facilitating the doctors' diagnosis.