Acoustic neuroma (AN) is a common benign tumor. Little is known of neuropsychological studies in patients with acoustic neuroma, especially cognitive neuropsychology, and the neuropsychological abnormalities of patients affect their life quality. The purpose of this study was to explore the changes in the cognitive function of patients with acoustic neuroma, and the possible mechanism of these changes by structural magnetic resonance imaging. We used a neuropsychological assessment battery to assess cognitive function in 69 patients with acoustic neuroma and 70 healthy controls. Then, we used diffusion tensor imaging data to construct the structural brain network and calculate topological properties based on graph theory, and we studied the relation between the structural brain network and cognitive function. Moreover, three different subnetworks (short-range subnetwork, middle-range subnetwork, and long-range subnetwork) were constructed by the length of nerve fibers obtained from deterministic tracking. We studied the global and local efficiency of various subnetworks and analyzed the correlation between network metrics and cognitive function. Furthermore, connectome edge analysis directly assessed whether there were differences in the number of fibers in the different brain regions. We analyzed the relation between the differences and cognitive function. Compared with the healthy controls, the general cognitive function, memory, executive function, attention, visual space executive ability, visual perception ability, movement speed, and information processing speed decreased significantly in patients with acoustic neuroma. A unilateral hearing loss due to a left acoustic neuroma had a greater impact on cognitive function. The results showed that changes in the global and local metrics, the efficiency of subnetworks, and cognitively-related fiber connections were associated with cognitive impairments in patients with acoustic neuroma. Patients exhibit cognitive impairments caused by the decline of the structure and function in some brain regions, and they also develop partial compensation after cognitive decline. Cognitive problems are frequent in patients with acoustic neuroma. Including neuropsychological aspects in the routine clinical evaluation and appropriate treatments may enhance the clinical management and improve their life quality.