A 70-year-old woman was referred to our hospital after a nodular shadow was noted on chest X-ray. Chest computed tomography showed a pulmonary mass in the right upper lobe, and brain magnetic resonance imaging revealed a right-sided frontal lobe tumor. A histological examination of a transbronchial lung biopsy specimen revealed adenocarcinoma with epidermal growth factor receptor mutations involving both exon 19 deletion and exon 20 insertion. After stereotactic radiotherapy for brain metastasis, the patient was treated with afatinib, which resulted in a complete response. We observed a case in which a patient had non-small cell lung cancer with compound EGFR mutations involving both exon 19 deletion and exon 20 insertion mutations that responded well to afatinib therapy.