Self-control failure has enormous personal and societal consequences. One of the most debated models explaining why self-control breaks down is the Strength Model, according to which self-control depends on a limited resource. Either previous acts of self-control or taking part in highly demanding cognitive tasks have been shown to reduce self-control, possibly due to a reduction in blood glucose levels. However, several studies yielded negative findings, and recent meta-analyses questioned the robustness of the depletion effect in humans. We investigated, for the first time, whether the Strength Model applies to a non-human primate species, the tufted capuchin monkey. We tested five capuchins in a self-control task (the Accumulation task) in which food items were accumulated within individual’s reach for as long as the subject refrained from taking them. We evaluated whether capuchins’ performance decreases: (i) when tested before receiving their daily meal rather than after consuming it (Energy Depletion Experiment), and (ii) after being tested in two tasks with different levels of cognitive complexity (Cognitive Depletion Experiment). We also tested, in both experiments, how implementing self-control in each trial of the Accumulation task affected this capacity within each session and/or across consecutive sessions. Repeated acts of self-control in each trial of the Accumulation task progressively reduced this capacity within each session, as predicted by the Strength Model. However, neither experiencing a reduction in energy level nor taking part in a highly demanding cognitive task decreased performance in the subsequent Accumulation task. Thus, whereas capuchins seem to be vulnerable to within-session depletion effects, to other extents our findings are in line with the growing body of studies that failed to find a depletion effect in humans. Methodological issues potentially affecting the lack of depletion effects in capuchins are discussed.