We provide a comprehensive diffusion MRI dataset acquired with a novel biomimetic phantom mimicking human white matter. The fiber substrates in the diffusion phantom were constructed from hollow textile axons ("taxons") with an inner diameter of 11.8±1.2 µm and outer diameter of 33.5±2.3 µm. Data were acquired on the 3 T CONNECTOM MRI scanner with multiple diffusion times and multiple q-values per diffusion time, which is a dedicated acquisition for validation of microstructural imaging methods, such as compartment size and volume fraction mapping. Minimal preprocessing was performed to correct for susceptibility and eddy current distortions. Data were deposited in the XNAT Central database (project ID: dMRI_Phant_MGH).