Hypertension is a risk factor for cognitive impairment in older age. However, evidence of the neural basis of the relationship between the deterioration of cognitive function and elevated blood pressure is sparse. Based on previous research, we speculate that variations in brain connectivity are closely related to elevated blood pressure even before the onset of clinical conditions and apparent cognitive decline in individuals over 60 years of age. Forty cognitively healthy adults were recruited. Each received a blood pressure test before and after the cognitive assessment in various domains. Diffusion tensor imaging (DTI) and resting-state functional magnetic resonance imaging (rsfMRI) data were collected. Our findings confirm that elevated blood pressure is associated with brain connectivity variations in cognitively healthy individuals. The integrity of the splenium of the corpus callosum is closely related to individual differences in systolic blood pressure. In particular, elevated systolic blood pressure is related to resting-state ventral attention network (VAN) and information processing speed. Serial mediation analyses have further revealed that lower integrity of the splenium statistically predicts elevated systolic blood pressure, which in turn predicts weakened functional connectivity (FC) within the VAN and eventually poorer processing speed. The current study sheds light on how neural correlates are involved in the impact of elevated blood pressure on cognitive functioning.