Diabetes can induce diseases including diabetic retinopathy, cataracts, glaucoma, etc. The blindness caused by these diseases is irreversible. Early analysis of retinal fundus images, including optic disc and optic cup detection and retinal blood vessel segmentation, can effectively identify these diseases. The existing methods lack sufficient discrimination power for the fundus image and are easily affected by pathological regions. This paper proposes a novel multi-path recurrent U-Net architecture to achieve the segmentation of retinal fundus images. The effectiveness of the proposed network structure was proved by two segmentation tasks: optic disc and optic cup segmentation and retinal vessel segmentation. Our method achieved state-of-the-art results in the segmentation of the Drishti-GS1 dataset. Regarding optic disc segmentation, the accuracy and Dice values reached 0.9967 and 0.9817, respectively; as regards optic cup segmentation, the accuracy and Dice values reached 0.9950 and 0.8921, respectively. Our proposed method was also verified on the retinal blood vessel segmentation dataset DRIVE and achieved a good accuracy rate.