A practical problem in supervised deep learning for medical image segmentation is the lack of labeled data which is expensive and time-consuming to acquire. In contrast, there is a considerable amount of unlabeled data available in the clinic. To make better use of the unlabeled data and improve the generalization on limited labeled data, in this paper, a novel semi-supervised segmentation method via multi-task curriculum learning is presented. Here, curriculum learning means that when training the network, simpler knowledge is preferentially learned to assist the learning of more difficult knowledge. Concretely, our framework consists of a main segmentation task and two auxiliary tasks, i.e. the feature regression task and target detection task. The two auxiliary tasks predict some relatively simpler image-level attributes and bounding boxes as the pseudo labels for the main segmentation task, enforcing the pixel-level segmentation result to match the distribution of these pseudo labels. In addition, to solve the problem of class imbalance in the images, a bounding-box-based attention (BBA) module is embedded, enabling the segmentation network to concern more about the target region rather than the background. Furthermore, to alleviate the adverse effects caused by the possible deviation of pseudo labels, error tolerance mechanisms are also adopted in the auxiliary tasks, including inequality constraint and bounding-box amplification. Our method is validated on ACDC2017 and PROMISE12 datasets. Experimental results demonstrate that compared with the full supervision method and state-of-the-art semi-supervised methods, our method yields a much better segmentation performance on a small labeled dataset. Code is available at https://github.com/DeepMedLab/MTCL.