This prospective clinical study assesses the feasibility of training a deep neural network (DNN) for intravoxel incoherent motion (IVIM) model fitting to diffusion-weighted MRI (DW-MRI) data and evaluates its performance. In May 2011, 10 male volunteers (age range, 29-53 years; mean, 37) underwent DW-MRI of the upper abdomen on 1.5T and 3.0T MR scanners. Regions of interest in the left and right liver lobe, pancreas, spleen, renal cortex, and renal medulla were delineated independently by 2 readers. DNNs were trained for IVIM model fitting using these data; results were compared to least-squares and Bayesian approaches to IVIM fitting. Intraclass correlation coefficients (ICCs) were used to assess consistency of measurements between readers. Intersubject variability was evaluated using coefficients of variation (CVs). The fitting error was calculated based on simulated data, and the average fitting time of each method was recorded. DNNs were trained successfully for IVIM parameter estimation. This approach was associated with high consistency between the 2 readers (ICCs between 50% and 97%), low intersubject variability of estimated parameter values (CVs between 9.2 and 28.4), and the lowest error when compared with least-squares and Bayesian approaches. Fitting by DNNs was several orders of magnitude quicker than the other methods, but the networks may need to be retrained for different acquisition protocols or imaged anatomical regions. DNNs are recommended for accurate and robust IVIM model fitting to DW-MRI data. Suitable software is available for download. © 2019 International Society for Magnetic Resonance in Medicine.