Diffusion tensor imaging (DTI) has been used to explore changes in the brain of subjects with human immunodeficiency virus (HIV) infection. However, DTI notoriously suffers from low specificity. Neurite orientation dispersion and density imaging (NODDI) is a compartmental model able to provide specific microstructural information with additional sensitivity/specificity. In this study we use both the NODDI and the DTI models to evaluate microstructural differences between 35 HIV-positive patients and 20 healthy controls. Diffusion-weighted imaging was acquired using three b-values (0, 1000 and 2500 s/mm2). Both DTI and NODDI models were fitted to the data, obtaining estimates for fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD), neurite density index (NDI) and orientation dispersion index (ODI), after which we performed group comparisons using Tract-based spatial statistics (TBSS). While significant group effects were found in in FA, MD, RD, AD and NDI, NDI analysis uncovered a much wider involvement of brain tissue in HIV infection as compared to DTI. In region-of interest (ROI)-based analysis, NDI estimates from the right corticospinal tract produced excellent performance in discriminating the two groups (AUC = 0.974, sensitivity = 90%; specificity =97%).