Respiratory motion and high magnetic fields pose challenges for quantitative diffusion weighted MRI (DWI) of mouse abdomen on preclinical MRI systems. EPI-based DWI method yields inadequate suppression of motion and magnetic susceptibility artifacts. Diffusion-weighted radial spin-echo (Rad-SE-DW) produces artifact-free images but require substantially longer acquisition times. Here, we demonstrate a new deep learning concept for accelerating acquisition of RAD-SE-DW. Fully sampled Rad-SE-DW images are used to train a convolution neural network for directly extracting apparent diffusion coefficient (ADC) maps from highly under-sampled Rad-SE-DW data. Comparisons with standard ADC extraction and acceleration methods are made to support this concept.