Retinal vascular diseases affect the well-being of human body and sometimes provide vital signs of otherwise undetected bodily damage. Recently, deep learning techniques have been successfully applied for detection of diabetic retinopathy (DR). The main obstacle of applying deep learning techniques to detect most other retinal vascular diseases is the limited amount of data available. In this paper, we propose a transfer learning technique that aims to utilize the feature similarities for detecting retinal vascular diseases. We choose the well-studied DR detection as a source task and identify the early detection of retinopathy of prematurity (ROP) as the target task. Our experimental results demonstrate that our DR-pretrained approach dominates in all metrics the conventional ImageNet-pretrained transfer learning approach, currently adopted in medical image analysis. Moreover, our approach is more robust with respect to the stochasticity in the training process and with respect to reduced training samples. This study suggests the potential of our proposed transfer learning approach for a broad range of retinal vascular diseases or pathologies, where data is limited.