The paradigm of leveraging large pre-trained language models has made significant progress on benchmarks on task-oriented dialogue (TOD) systems. In this paper, we combine this paradigm with multi-task learning framework for end-to-end TOD modeling by adopting span prediction as an auxiliary task. In end-to-end setting, our model achieves new state-of-the-art results with combined scores of 108.3 and 107.5 on MultiWOZ 2.0 and MultiWOZ 2.1, respectively. Furthermore, we demonstrate that multi-task learning improves not only the performance of model but its generalization capability through domain adaptation experiments in the few-shot setting. The code is available at github.com/bepoetree/MTTOD.