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Abstract The biological processes involved in a drug’s mechanisms of action are oftentimes dynamic, complex and difficult to discern. Time-course gene expression data is a rich source of information that can be used to unravel these complex processes, identify biomarkers of drug sensitivity and predict the response to a drug. However, the majority of previous work has not fully utilized this temporal dimension. In these studies, the gene expression data is either considered at one time-point (before the administration of the drug) or two time-points (before and after the administration of the drug). This is clearly inadequate in modeling dynamic gene–drug interactions, especially for applications such as long-term drug therapy. In this work, we present a novel REcursive Prediction (REP) framework for drug response prediction by taking advantage of time-course gene expression data. Our goal is to predict drug response values at every stage of a long-term treatment, given the expression levels of genes collected in the previous time-points. To this end, REP employs a built-in recursive structure that exploits the intrinsic time-course nature of the data and integrates past values of drug responses for subsequent predictions. It also incorporates tensor completion that can not only alleviate the impact of noise and missing data, but also predict unseen gene expression levels (GEXs). These advantages enable REP to estimate drug response at any stage of a given treatment from some GEXs measured in the beginning of the treatment. Extensive experiments on two datasets corresponding to multiple sclerosis patients treated with interferon are included to showcase the effectiveness of REP.