Nasopharyngeal Carcinoma (NPC) is a worldwide malignant epithelial cancer. Survival prediction is a major concern for NPC patients, as it provides early prognostic information that is needed to guide treatments. Recently, deep learning, which leverages Deep Neural Networks (DNNs) to learn deep representations of image patterns, has been introduced to the survival prediction in various cancers including NPC. It has been reported that image-derived end-to-end deep survival models have the potential to outperform clinical prognostic indicators and traditional radiomics-based survival models in prognostic performance. However, deep survival models, especially 3D models, require large image training data to avoid overfitting. Unfortunately, medical image data is usually scarce, especially for Positron Emission Tomography/Computed Tomography (PET/CT) due to the high cost of PET/CT scanning. Compared to Magnetic Resonance Imaging (MRI) or Computed Tomography (CT) providing only anatomical information of tumors, PET/CT that provides both anatomical (from CT) and metabolic (from PET) information is promising to achieve more accurate survival prediction. However, we have not identified any 3D end-to-end deep survival model that applies to small PET/CT data of NPC patients. In this study, we introduced the concept of multi-task leaning into deep survival models to address the overfitting problem resulted from small data. Tumor segmentation was incorporated as an auxiliary task to enhance the models efficiency of learning from scarce PET/CT data. Based on this idea, we proposed a 3D end-to-end Deep Multi-Task Survival model (DeepMTS) for joint survival prediction and tumor segmentation. Our DeepMTS can jointly learn survival prediction and tumor segmentation using PET/CT data of only 170 patients with advanced NPC.