Mutations in the gene encoding epidermal growth factor receptor (EGFR) are the most frequent driver mutations in lung adenocarcinoma in Japan. Exon 19 deletion and L858R mutation in exon 21 are the most common EGFR mutations. Uncommon mutations, such as G719X, S768I, and L861Q, and compound mutations, combinations of 2 common or uncommon mutations, have also been reported. EGFR tyrosine kinase inhibitors (TKIs) are effective against cancers harboring common mutations; however, their efficacy against cancers with uncommon or compound mutations remains unclear. We report the case of a 67-year-old man with lung adenocarcinoma (clinical stage IIIA [cT1N2M0]), harboring an uncommon compound mutation, G719X and S768I. The cancer progressed within 2 months of initial chemoradiotherapy. Treatment with afatinib (40 mg/day) produced a partial response, which was maintained for 17 months with continued treatment. A literature review revealed that lung cancer with G719X/S768I compound mutation exhibited good response to EGFR-TKIs, even better than that of lung cancers with single uncommon mutations.