Retinopathy of prematurity infants is an angiogenic disease. It is one of the main causes of neonatal retina damage or blindness. By segmenting and analyzing the structure of fundus vessels, early diagnosis and monitoring of retinopathy of prematurity infants can be performed. Compared with adult retinal vessels, those of prematurity infants have lower contrast and choroid overlap, which leads to low accuracy and sensitivity of retinal vessel segmentation. Therefore, the FDMU-net neonatal retinal segmentation model is proposed under the U-net framework. The model incorporates dense connection layers to improve feature utilization. During encoding and decoding channel stitching, multi-scale convolution kernels are used to fuse features, which improve the receptive field. Finally, the weighted focal loss of the vessel skeleton is used as a loss function to improve the network’s problem of poor segmentation of fuzzy samples. The algorithm proposed in this paper was tested on two public datasets, DRIVE and STARE, with an accuracy of 96.75% and 96.85%, and sensitivity of 81.52% and 84.84%, respectively. Moreover, after performing experiments on the fundus dataset of prematurity infants, compared with the U-net model, the AttentionResU-Net model and the multi-scale feature fusion full convolutional neural network model, the proposed FDMU-net model has higher accuracy and sensitivity. In conclusion, the algorithm proposed in this paper can satisfactorily solve the problems of vessel loss and low sensitivity in vessel segmentation and effectively segment the retinal vessel of prematurity infants.