This paper proposes a fast eye detection method based on fully-convolutional Siamese networks for iris recognition. The iris on the move system requires to capture high resolution iris images from a moving subject for iris recognition. Therefore, capturing images contains both eyes at high-frame-rate increases the chance of iris imaging. In order to output the authentication result in real time, the system requires a fast eye detector extracting the left and right eye regions from the image. Our method extracts features of a partial face image and a reference eye image using Siamese network frameworks. Similarity heat maps of both eyes are created by calculating the spatial cosine similarity between extracted features. Besides, we use CosFace as a loss function for training to discriminate the left and right eyes with high accuracy even with a shallow network. Experimental results show that our method trained by CosFace is fast and accurate compared with conventional generic object detection methods.