• President – Chiang Kai-shek, Yen Chia-kan
• Vice President – Yen Chia-kan, Chiang Ching-kuo
• Premier – Chiang Ching-kuo
• Vice Premier – Hsu Ching-chung

February edit

• 10 February – The opening of Chinese Culture and Movie Center in Taipei.

April edit

• 5 April – President Chiang Kai-shek died in age 87, Yen Chia-kan became the President of the Republic of China.

July edit

• 8 July – The establishment of diplomatic relations with Paraguay.
• 26 July – The opening of Beipu Station of Taiwan Railways Administration in Xincheng Township, Hualien County.

December edit

• 20 December – 1975 Republic of China legislative election.

• 28 February – A-Sun, singer and songwriter
• 19 March – Vivian Hsu, singer, actress and model
• 9 May – Weng Li-you, pop singer
• 27 May – Lin Chih-chien, Mayor of Hsinchu City
• 6 June – Cheer Chen, singer and songwriter
• 9 June – Serina Liu, actress (d. 2020)
• 1 July – Kung Tsui-chang, Duke Yansheng
• 5 October – Hsieh Kuo-liang, member of 6th, 7th and 8th Legislative Yuan
• 15 October – Hsu Shu-hua, member of Legislative Yuan
• 5 December – Laha Mebow, writer, producer and director
• 10 December – Hsing Hui, actress

• 26 February – Li Hsi-mou, 79, former President of Taiwan Provincial Museum
• 5 April – Chiang Kai-shek, 87, President
• 23 December – Chen Pao-pei, table tennis player