Recommender systems are frequently used in domains in which users express their preferences in the form of graded judgments, such as ratings. If accurate top-N recommendation lists are to be produced for such graded relevance domains, it is critical to generate a ranked list of recommended items directly rather than predicting ratings. Current techniques choose one of two sub-optimal approaches: either they optimize for a binary metric such as Average Precision, which discards information on relevance grades, or they optimize for Normalized Discounted Cumulative Gain (NDCG), which ignores the dependence of an item's contribution on the relevance of more highly ranked items. In this paper, we address the shortcomings of existing approaches by proposing the Graded Average Precision factor model (GAPfm), a latent factor model that is particularly suited to the problem of top-N recommendation in domains with graded relevance data. The model optimizes for Graded Average Precision, a metric that has been proposed recently for assessing the quality of ranked results list for graded relevance. GAPfm learns a latent factor model by directly optimizing a smoothed approximation of GAP. GAPfm's advantages are twofold: it maintains full information about graded relevance and also addresses the limitations of models that optimize NDCG. Experimental results show that GAPfm achieves substantial improvements on the top-N recommendation task, compared to several state-of-the-art approaches. In order to ensure that GAPfm is able to scale to very large data sets, we propose a fast learning algorithm that uses an adaptive item selection strategy. A final experiment shows that GAPfm is useful not only for generating recommendation lists, but also for ranking a given list of rated items.