The aim was to investigate the association of parental education at birth with cognitive ability in childhood and young adulthood and determine, whether functional connectivity of the salience network underlies this association. We studied participants of the Czech arm of the European Longitudinal Study of Pregnancy and Childhood who underwent assessment of their cognitive ability at age 8 (Wechsler Intelligence Scale for Children) and 28/29 years (Wechsler Adult Intelligence Scale) and measurement with resting state functional MRI at age 23/24. We estimated the associations of parental education with cognitive ability and functional connectivity between the seeds in the salience network and other voxels in the brain. We found that lower education of both mothers and fathers was associated with lower verbal IQ, performance IQ and full-scale IQ of the offspring at age 8. Only mother´s education was associated with performance IQ at age 28/29. Lower mother´s education correlated with greater functional connectivity between the right rostral prefrontal cortex and a cluster of voxels in the occipital cortex, which, in turn, was associated with lower performance IQ at age 28/29. We conclude that the impact of parental education, particularly father´s, on offspring´s cognitive ability weakens during the lifecourse. Functional connectivity between the right rostral prefrontal cortex and occipital cortex may be a biomarker underlying the transmission of mother´s education on performance IQ of their offspring.