The yield of premium green tea is reduced when the plants are exposed to abnormally low temperatures caused by climate change. In particular, the damage caused by frost is severe. All frost-damaged tea leaves are discarded after pruning. This study was conducted to partially reduce the decrease in farm household income caused by frost damage using these damaged tea leaves for black tea processing. Frost-damaged tea leaves were harvested in May 2022 and processed into black tea. The changes in the component content were investigated by analyzing the catechin, caffeine, theaflavin, and free amino acids and performing taste analysis using an electronic tongue. The total catechin content was 0.24% and 1.06% in the undamaged and frost-damaged black tea, respectively. The C (catechin) content was particularly high at 0.81% in the frost-damaged black tea. The caffeine levels in undamaged and frost-damaged black tea were 0.84% and 0.42%, respectively, showing an approximately 50% reduction of the caffeine content by frost damage. The total theaflavin content in undamaged and frost-damaged black tea was 0.24% and 0.13%, respectively. The total free amino acid content in undamaged and frost-damaged black tea was 714 mg/100 g and 1,122 mg/100 g, respectively, of which the γ-aminobutyric acid content in undamaged and frost-damaged black tea was 16.9 mg/100 g and 140.4 mg/100 g, respectively. Taste analysis using the electronic tongue revealed high AHS and CPS sensor values in undamaged black tea and high CTS, PKS, NMS, and SCS sensor values in frost-damaged black tea.