The detection of the optic disc (OD) and fovea is essential to many automatic diagnosis systems for retinal diseases. The single shot multibox detector (SSD) can generate predictions from feature maps of various resolutions, which has not been introduced into the OD and fovea detection. To enhance the detection performance, we propose an improved SSD network, which has strengthened information flow enabled by the dense connections. The proposed method can achieve multiscale detection of the OD and fovea with strengthened feature propagation. Extensive experiments on the publicly available Messidor database and local fundus images are performed to evaluate the performance of the proposed method. Compared with seven types of representative solutions in the Messidor database, the proposed method can achieve competitive performance compared to state-of-the-art algorithms. Furthermore, the proposed method is applied to the excyclotropia screening. The screening results demonstrate promising application prospects for the proposed method in medical practice.