Binary user-behavior logs such as clicks or views, called implicit feedback, are often used to build recommender systems because of its general availability in real practice. Most existing studies formulate implicit feedback as binary relevance feedback. However, in numerous applications, implicit feedback is observed not only as a binary indicator but also in a graded form, such as the number of clicks and the dwell time observed after a click, which we call the graded implicit feedback. The grade information should appropriately be utilized, as it is considered a more direct relevance data compared to the mere implicit feedback. However, a challenge is that the grade information is observed only for the user–item pairs with implicit feedback, whereas the grade information is unobservable for the pairs without implicit feedback. Moreover, graded implicit feedback for some user–item pairs is more likely to be observed than for others, resulting in the missing-not-at-random (MNAR) problem. To the best of our knowledge, graded implicit feedback under the MNAR mechanism has not yet been investigated despite its prevalence in real-life recommender systems. In response, we formulate a recommendation with graded implicit feedback as a statistical estimation problem and define an ideal loss function of interest, which should ideally be optimized to maximize the user experience. Subsequently, we propose an unbiased estimator for the ideal loss, building on the inverse propensity score estimator. Finally, we conduct an empirical evaluation of the proposed method on a public real-world dataset.