The asymptomatic phase of familial Alzheimer’s disease caused by E280A mutation in presenilin-1 gene is characterized by intact performance in traditional neuropsychological tasks including memory, language, and executive functions. However, asymptomatic mutation carriers are already impaired in tasks that require visual short-term memory binding. Meanwhile, neuropathological changes in white matter integrity take place during the course of familial Alzheimer’s disease. We investigated whether the behavioural short-term memory binding deficits are accompanied by changes in white matter integrity in asymptomatic and clinical phases of familial Alzheimer’s disease. Three groups - asymptomatic carriers of presenilin-1 gene mutation, familial Alzheimer’s disease patients, and healthy controls - underwent an assessment consisting of a neuropsychological test battery, two visual short-term memory binding tasks, and diffusion tensor imaging. Group comparisons indicated changes in white matter integrity in familial Alzheimer’s disease patients and to smaller extent already in asymptomatic carriers. Higher performance in visual shape-colour binding task was related to higher white matter integrity in frontal areas, and higher performance in visual colour-colour binding task was related to higher white matter integrity in frontal and parietal areas. Thus, we demonstrate the early changes in white matter integrity already in asymptomatic phase of familial Alzheimer’s disease. These changes become more widespread in the course of the disease. In addition, impaired performance in visual short-term memory binding tasks is accompanied by changes in white matter integrity which might implicate loss of connectivity. The results help to shed light on the neural underpinnings of familial Alzheimer’s disease and might lead to development of new methods for the early diagnosis of Alzheimer’s disease.