For single-image super-resolution, constructing an appropriate observation model is a significant but unnoticed attempt to super-resolve the low-resolution image. Observation model describes the process that how the low-resolution image degrades from a high-resolution image. The traditional observation model takes the assumption that the low-resolution image is suffered from noising, blurring, and down-sampling, and it is widely used in the super-resolution field. In fact, these factors usually result to some information lost during the degradation process, however, the missing information goes beyond the widely used observation model, which makes single-image super-resolution highly ill-posed. To solve this issue, we have to consider the question, “what is being ignored in the degradation process?” In this paper, we propose a novel framework by extending typical degradation-based single-image super-resolution with a plug-and-play method to handle the low-resolution image obtained in more complex real scenes. Specifically, a new observation model is designed to describe the degradation process more reasonably. To optimize the corresponding induced energy function, a plug-and-play super-resolution algorithm is derived based on the half splitting quadratic technique, which allows us to insert a learned denoising model as a modular part. The quantitative and qualitative evaluations illustrate the superiority of the proposed method for detail preservation and noise removal over state-of-the-art algorithms.