The most common biochemical defect in Leigh syndrome is aberrations in proteins involved in the assembly of the subunits of complex IV of the electron transport chain (ETC)—cytochrome C oxidase (COX) in the mitochondrial membrane. Among these, mutations in the SURF1 gene are the most common. The SURF1 protein (Sea Urchin Retroposon Family 1) is embedded in the inner mitochondrial membrane and plays a crucial role in the assembly of the COX complex. All mutations in the SURF1 gene result in the biosynthesis of a truncated protein and damage to the COX complex. Adeno-associated viral vectors (AAV9), which carry the not mutated SURF1 gene, are being investigated for the treatment of this disease. The aim of this study was to evaluate the expression levels of SURF1 and MTCO1 proteins in whole blood from patients with Leigh syndrome compared to reference values obtained for a pool of patients without mutations, as well as to evaluate the expression of the MTCO1 cytochrome c oxidase subunit in skin fibroblast cultures from patients with SURF1-associated Leigh syndrome treated with AAV9. To investigate the gene therapy efficacy, an adenovirus construct with a normal counterpart was added to fibroblasts derived from the skin of a patient with a mutation in the Surf1 gene and to control skin fibroblasts at an optimal dose that did not impair cell viability in the MTT assay. We used Western blot analysis and quantitative PCR to evaluate changes in the relative amounts of the studied proteins after the addition of AAV9 to control cells and cells obtained from the patient and identified significant compensatory changes in skin fibroblasts from a patient with a SURF1 mutation.