Diabetic retinopathy (DR), caused by damage to the blood vessels in the tissue of the retina, is a  microvascular complication of diabetes. DR is the leading cause of vision loss among working-aged adults. However, due to the low compliance rate of DR screening and expensive medical devices for ophthalmic exams, many DR patients did not seek proper medical attention until DR develops to irreversible stages (i.e., vision loss). Fortunately, the widely available electronic health record (EHR) databases provide an unprecedented opportunity to develop cost-effective machine-learning tools for DR detection. This paper proposes a Multi-branching Temporal Convolutional Network with Tensor Data Completion (MB-TCN-TC) model to analyze the longitudinal EHRs collected from diabetic patients for DR prediction. Experimental results demonstrate that the proposed MB-TCN-TC model not only effectively copes with the imbalanced data and missing value issues commonly seen in EHR datasets but also captures the temporal correlation and complicated interactions among medical variables in the longitudinal clinical records, yielding superior prediction performance compared to existing methods.