Objectives: Alexander disease (AxD) is a rare neurodegenerative disorder that represents a group of leukodystrophies with severe disability and premature death, mostly with an infancy/childhood onset. In rare cases of late-onset phenotypes, symptoms are often milder and difficult to diagnose. We present a diagnostic journey of a teenage male patient with a progressive gait disorder starting at the age of 13 years, with a final diagnosis of Alexander disease. Early in the course of the disease, the boy exhibited distinctive cognitive involvement and neuropsychological deterioration characterized by selective impairment of visual and long-term auditory memory, along with a decline in IQ but preserved reasoning abilities. Methods: The patient underwent an extensive neurological diagnostic workup, which included magnetic resonance imaging (MRI) of the brain, spine, and abdomen, as well as electrophysiological, metabolic, and biochemical tests. Numerous specialist consultations were conducted, including genetic, cardiology, ophthalmology, pulmonology, oncohematology, psychological, and speech-language pathology consultations. In addition, a focused literature review was performed using PubMed, Scopus, Web of Science, and Google Scholar with the search terms Alexander disease, GFAP gene, late-onset, spastic paraplegia and GFAP variant p/Gly18Val. Results: Whole exome sequencing revealed an extremely rare missense GFAP heterozygous variant NM_002055.5: c.54G>T (p/Gly18Val), confirming the diagnosis of AxD. Conclusions: The presented case highlights the importance of whole-exome sequencing in the diagnosis of unexplained otherwise neurological symptoms, such as progressive spastic paraplegia.