Medical image segmentation is a vital stage in medical image analysis. Numerous deep-learning methods are booming to improve the performance of 2-D medical image segmentation, owing to the fast growth of the convolutional neural network. Generally, the manually defined ground truth is utilized directly to supervise models in the training phase. However, direct supervision of the ground truth often results in ambiguity and distractors as complex challenges appear simultaneously. To alleviate this issue, we propose a gradually recurrent network with curriculum learning, which is supervised by gradual information of the ground truth. The whole model is composed of two independent networks. One is the segmentation network denoted as GREnet, which formulates 2-D medical image segmentation as a temporal task supervised by pixel-level gradual curricula in the training phase. The other is a curriculum-mining network. To a certain degree, the curriculum-mining network provides curricula with an increasing difficulty in the ground truth of the training set by progressively uncovering hard-to-segmentation pixels via a data-driven manner. Given that segmentation is a pixel-level dense-prediction challenge, to the best of our knowledge, this is the first work to function 2-D medical image segmentation as a temporal task with pixel-level curriculum learning. In GREnet, the naive UNet is adopted as the backbone, while ConvLSTM is used to establish the temporal link between gradual curricula. In the curriculum-mining network, UNet ++ supplemented by transformer is designed to deliver curricula through the outputs of the modified UNet ++ at different layers. Experimental results have demonstrated the effectiveness of GREnet on seven datasets, i.e., three lesion segmentation datasets in dermoscopic images, an optic disc and cup segmentation dataset and a blood vessel segmentation dataset in retinal images, a breast lesion segmentation dataset in ultrasound images, and a lung segmentation dataset in computed tomography (CT).