Diabetic Foot Ulcer (DFU) is a major complication of Diabetes, which if not managed properly can lead to amputation. DFU can appear anywhere on the foot and can vary in size, colour, and contrast depending on various pathologies. Current clinical approaches to DFU treatment rely on patients and clinician vigilance, which has significant limitations such as the high cost involved in the diagnosis, treatment and lengthy care of the DFU. We introduce a dataset of 705 foot images. We provide the ground truth of ulcer region and the surrounding skin that is an important indicator for clinicians to assess the progress of ulcer. Then, we propose a two-tier transfer learning from bigger datasets to train the Fully Convolutional Networks (FCNs) to automatically segment the ulcer and surrounding skin. Using 5fold cross-validation, the proposed two-tier transfer learning FCN Models achieve a Dice Similarity Coefficient of 0.794 (±0.104) for ulcer region, 0.851 (±0.148) for surrounding skin region, and 0.899 (±0.072) for the combination of both regions. This demonstrates the potential of FCNs in DFU segmentation, which can be further improved with a larger dataset.