In this work we propose a method that integrates multi-task learning (MTL) and deep learning. Our method appends a MTL-like loss to a deep convolutional neural network, in order to learn the relations between tasks together at the same time, and also incorporates the label correlations between pairs of tasks. We apply the proposed method on a transfer learning scenario, where our objective is to fine-tune the parameters of a network that has been originally trained on a large-scale image dataset for concept detection, so that it be applied on a target video dataset and a corresponding new set of target concepts. We evaluate the proposed method for the video concept detection problem on the TRECVID 2013 Semantic Indexing dataset. Our results show that the proposed algorithm leads to better concept-based video annotation than existing state-of-the-art methods.