Purpose: The differential diagnosis of glioblastoma (GBM) versus single brain metastasis (Met) is clinically important, and is undertaken with a clinical reading of MR images and/or tumor biopsy. We investigate whether Mets and GBMs can be differentiated based on the microstructure of the FLAIR-hyperintense peritumoral region measured by diffusion tensor imaging (DTI). We hypothesize that the peritumoral microstructure differs in extracellular water content, based on whether it is vasogenic edema or infiltrative. We use deep learning trained on DTI-based free-water volume fraction maps to discriminate between the peritumoral regions of Met and GBM neoplasms. Our results are also compared with mean diffusivity (MD), the most commonly used DTI metric. Method: dMRI data of 143 patients with brain tumors (89 glioblastomas and 54 metastases, ages 19-87 years, 77 females and 66 males) were included. Free-water volume fraction maps were computed for the peritumoral regions (demarcated automatically). We developed a 7-layer convolutional neural network (CNN) architecture to distinguish microstructural patterns of Met and GBM tumors using 32 x 32 mm patches placed at random in the peritumoral area. The CNN was trained on patches from a training set of 113 patients and tested on the remaining 30 patients, where majority voting was applied to predict the tumor type for each patient. Although MD has been previously used in both tumor and peritumoral area for discriminating tumor type, we replicated the same process with MD only in the peritumoral area to provide a stronger comparison. RESULT: We predicted tumor type with 93% accuracy, outperforming MD with 84% accuracy. Conclusion: Our results demonstrate that deep learning with CNN on DTI-based free-water volume fraction map can be a promising tool for automatic distinction of tumor types, and has potential as a tumor biomarker.