The aim of dynamic prediction is to provide individualized risk predictions over time, which are updated as new data become available. In pursuit of constructing a dynamic prediction model for a progressive eye disorder, age-related macular degeneration (AMD), we propose a time-dependent Cox survival neural network (tdCoxSNN) to predict its progression using longitudinal fundus images. tdCoxSNN builds upon the time-dependent Cox model by utilizing a neural network to capture the non-linear effect of time-dependent covariates on the survival outcome. Moreover, by concurrently integrating a convolutional neural network (CNN) with the survival network, tdCoxSNN can directly take longitudinal images as input. We evaluate and compare our proposed method with joint modeling and landmarking approaches through extensive simulations. We applied the proposed approach to two real datasets. One is a large AMD study, the Age-Related Eye Disease Study (AREDS), in which more than 50,000 fundus images were captured over a period of 12 years for more than 4,000 participants. Another is a public dataset of the primary biliary cirrhosis (PBC) disease, where multiple lab tests were longitudinally collected to predict the time-to-liver transplant. Our approach demonstrates commendable predictive performance in both simulation studies and the analysis of the two real datasets.