In this paper, we propose an image quality transformer (IQT) that successfully applies a transformer architecture to a perceptual full-reference image quality assessment (IQA) task. Perceptual representation becomes more important in image quality assessment. In this context, we extract the perceptual feature representations from each of input images using a convolutional neural network (CNN) backbone. The extracted feature maps are fed into the transformer encoder and decoder in order to compare a reference and distorted images. Following an approach of the transformer-based vision models, we use extra learnable quality embedding and position embedding. The output of the transformer is passed to a prediction head in order to predict a final quality score. The experimental results show that our proposed model has an outstanding performance for the standard IQA datasets. For a large-scale IQA dataset containing output images of generative model, our model also shows the promising results. The proposed IQT was ranked first among 13 participants in the NTIRE 2021 perceptual image quality assessment challenge. Our work will be an opportunity to further expand the approach for the perceptual IQA task.