Ten percent of non-small cell lung cancer patients with epidermal growth factor receptor (EGFR) mutations harbor uncommon variants. These mutations are mainly involved in lung adenocarcinomas but are rare in lung squamous cell carcinoma (LSCC). In 2018, the Food and Drug Administration-approved afatinib for this specific patient population. However, there is limited information regarding the effectiveness of afatinib for LSCC with EGFR mutations. This case report documented a unique case of a patient with LSCC, which had a rare compound EGFR mutation (G719C and S768I) and showed significant response to afatinib treatment, with 10 months of progression-free survival. New NTRK1 and RET gene mutations may play a potential role in the development of acquired resistance to afatinib following clinical progression. This case highlights the importance of genetic profiling in patients with LSCC. Although these patients have a low positive rate of EGFR mutations, searching for EGFR mutations in these patients might broaden their treatment options.