Iris recognition is a biometric technique which uses unique iris patterns between the pupil and sclera. The advantage of iris recognition lies in high recognition accuracy; however, for good performance, it requires the diameter of the iris to be greater than 200 pixels in an input image. So, a conventional iris system uses a camera with a costly and bulky zoom lens. To overcome this problem, we propose a new method to restore a low resolution iris image into a high resolution image using a single image. This study has three novelties compared to previous works: (i) To obtain a high resolution iris image, we only use a single iris image. This can solve the problems of conventional restoration methods with multiple images, which need considerable processing time for image capturing and registration. (ii) By using bilinear interpolation and a constrained least squares (CLS) filter based on the degradation model, we obtain a high resolution iris image with high recognition performance at fast speed. (iii) We select the optimized parameters of the CLS filter and degradation model according to the zoom factor of the image in terms of recognition accuracy. Experimental results showed that the accuracy of iris recognition was enhanced using the proposed method.