Image quality assessment (IQA) is an important research topic for understanding and improving visual experience. The current state-of-the-art IQA methods are based on convolutional neural networks (CNNs). The performance of CNN-based models is often compromised by the fixed shape constraint in batch training. To accommodate this, the input images are usually resized and cropped to a fixed shape, causing image quality degradation. To address this, we design a multi-scale image quality Transformer (MUSIQ) to process native resolution images with varying sizes and aspect ratios. With a multi-scale image representation, our proposed method can capture image quality at different granularities. Furthermore, a novel hash-based 2D spatial embedding and a scale embedding is proposed to support the positional embedding in the multi-scale representation. Experimental results verify that our method can achieve state-of-the-art performance on multiple large scale IQA datasets such as PaQ-2-PiQ, SPAQ, and KonIQ-10k.