(1) Background: We analyzed, using PET-SCAN and cognitive tests, how growth hormone (GH) could act in the brain of an older woman, not deficient in GH, who showed mild cognitive alterations (MCI) and had a genotype of ApoE 4/3 and familial dyslipidemia. (2) Methods: After performing a first psychometric study (TAVEC verbal learning test), the metabolic activity of brain structures related to knowledge, memory, and behavior was analyzed using 18-F fluorodeoxyglucose PET-SCAN. The patient was then treated with GH (0.4 mg/day, subcutaneous) for three weeks and on the last day under this treatment, a new PET-SCAN was performed. One month after beginning treatment with GH, a new TAVEC test was performed. (3) Results: GH administration normalized the cognitive deficits observed in the first psychometric test and significantly (p < 0.025) increased the metabolic activity in practically all brain cortical areas, specifically in the left hippocampus and left amygdala, although not in the left parahippocampus. (4) Conclusions: This study demonstrates for the first time the positive effects of GH on cerebral metabolism in a patient without GH deficiency, recovering the function of affected areas related to knowledge, memory, and behavior in an elderly patient with MCI.