Children suffering from conductive or mixed hearing loss may benefit from a bone-anchored hearing aid system (BAHA Attract implantable prosthesis). After audiological rehabilitation, different aspects of development are improving. The objective of this case report is to propose a comprehensive framework for monitoring cortical auditory function after implantation of a bone-anchored hearing aid system by using electrophysiological and neuropsychological measurements. We present the case of a seven-year-old boy with a congenital hearing loss due to a plurimalformative syndrome, including outer and middle ear malformation. After the diagnosis of hearing loss and the audiological rehabilitation with a BAHA Attract implantable prosthesis, the cortical auditory evoked potentials were recorded. We performed a neuropsychological evaluation using the Wechsler Intelligence Scale for Children - Fourth Edition, which was applied according to a standard procedure. The P1 latency was delayed according to the age (an objective biomarker for quantifying cortical auditory function). The neuropsychological evaluation revealed that the child's working memory and verbal reasoning abilities were in the borderline range comparing with his nonverbal reasoning abilities and processing abilities, which were in the average and below-average range, respectively. Cortical auditory evoked potentials, along with neuropsychological evaluation, could be an essential tool for monitoring cortical auditory function in children with hearing loss after a bone-anchored hearing aid implantation.