The new coronavirus, which has become a global pandemic, has confirmed more than 88 million cases worldwide since the first case was recorded in December 2019, causing over 1.9 million deaths. Since COIVD-19 lesions have clear imaging features on CT images, it is suitable for the auxiliary diagnosis and treatment of COVID-19. Deep learning can be used to segment the lesions areas of COVID-19 in CT images to help monitor the epidemic situation. In this paper, we propose a multi-point supervision network (MPS-Net) for segmentation of COVID-19 lung infection CT image lesions to solve the problem of a variety of lesion shapes and areas. A multi-scale feature extraction structure, a sieve connection structure (SC), a multi-scale input structure and a multi-point supervised training structure were implemented into MPS-Net. In order to increase the ability to segment various lesion areas of different sizes, the multi-scale feature extraction structure and the sieve connection structure will use different sizes of receptive fields to extract feature maps of various scales. The multi-scale input structure is used to minimize the edge loss caused by the convolution process. In order to improve the accuracy of segmentation, we propose a multi-point supervision training structure to extract supervision signals from different upsampling points on the network. Experimental results showed that the dice similarity coefficient (DSC), sensitivity, specificity and IOU of the segmentation results of our model are 0.8325, 0.8406, 09988 and 0.742, respectively. The experimental results demonstrated that the network proposed in this paper can effectively segment COVID-19 infection on CT images. It can be used to assist the diagnosis and treatment of new coronary pneumonia.