Quality assessment driven by machine learning generally relies on the strong assumption that the training and testing data share very close scene statistics, lacking the adaptation capacity to the content in other domains. In this paper, we quest the capability of transferring the quality of natural scene to the images that are not acquired by optical cameras (e.g., screen content images, SCIs), rooted in the widely accepted view that the human visual system has adapted and evolved through the perception of natural environment. Here we develop the first unsupervised domain adaptation based no reference quality assessment method, under the reasonable assumption that there are abundant subjective ratings of natural images (NIs). In general, it is a non-trivial task to directly transfer the quality prediction model from NIs to a new type of content (i.e., SCIs) that holds dramatically different statistical characteristics. Inspired by the transferability of pair-wise relationship, the proposed quality measure operates based on the philosophy of learning to rank. To reduce the domain gap, we introduce two complementary losses which explicitly regularize the feature space of ranking in a progressive manner. For feature discrepancy minimization, the maximum mean discrepancy (MMD) is imposed on the extracted ranking features of NIs and SCIs. For feature discriminatory capability enhancement, we propose a center based loss to rectify the classifier and improve its prediction capability not only for source domain (NI) but also the target domain (SCI). Experiments show that our method can achieve higher performance on different source-target settings based on a light-weight convolution neural network. The proposed method also sheds light on learning quality assessment measures for unseen application-specific content without the cumbersome and costing subjective evaluations.