Apathy is a syndrome of reduced motivation that commonly occurs in patients with cerebral small vessel disease, including those with the early onset form, CADASIL (cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy). The cognitive mechanisms underlying apathy are poorly understood and treatment options are limited. We hypothesized that disrupted effort-based decision-making, the cognitive process by which potential rewards and the effort cost required to obtain them is integrated to drive behaviour, might underlie the apathetic syndrome. Nineteen patients with a genetic diagnosis of CADASIL, as a model of 'pure' vascular cognitive impairment, and 19 matched controls were assessed using two different behavioural paradigms and MRI. On a decision-making task, participants decided whether to accept or reject sequential offers of monetary reward in return for exerting physical effort via handheld dynamometers. Six levels of reward and six levels of effort were manipulated independently so offers spanned the full range of possible combinations. Choice, decision time and force metrics were recorded. Each participant's effort and reward sensitivity was estimated using a computational model of choice. On a separate eye movement paradigm, physiological reward sensitivity was indexed by measuring pupillary dilatation to increasing monetary incentives. This metric was related to apathy status and compared to the behavioural metric of reward sensitivity on the decision-making task. Finally, high quality diffusion imaging and tract-based spatial statistics were used to determine whether tracts linking brain regions implicated in effort-based decision-making were disrupted in apathetic patients. Overall, apathetic patients with CADASIL rejected significantly more offers on the decision-making task, due to reduced reward sensitivity rather than effort hypersensitivity. Apathy was also associated with blunted pupillary responses to incentives. Furthermore, these independent behavioural and physiological markers of reward sensitivity were significantly correlated. Non-apathetic patients with CADASIL did not differ from controls on either task, whilst actual motor performance of apathetic patients in both tasks was also normal. Apathy was specifically associated with reduced fractional anisotropy within tracts connecting regions previously associated with effort-based decision-making. These findings demonstrate behavioural, physiological and anatomical evidence that dysfunctional effort-based decision-making underlies apathy in patients with CADASIL, a model disorder for sporadic small vessel disease. Reduced incentivization by rewards rather than hypersensitivity to effort costs drives this altered pattern of behaviour. The study provides empirical evidence of a cognitive mechanism for apathy in cerebral small vessel disease, and identifies a promising therapeutic target for interventions to improve this debilitating condition.