The son of a Christian minister, Yu was taught the Chinese classics as a child. He also studied at Boone University in Wuchang and at St. John's University in Shanghai. He graduated with a Bachelor of Arts degree from the latter in 1905 and obtained his master's from Harvard University, USA, in 1910.
Upon his return to China, he became headmaster of Boone School in Wuchang and was briefly commissioner for foreign affairs in Hubei. In 1912 he became associate editor of the Peking Daily News. He was also a private secretary to Li Yuanhong, first vice president of the new government in Beijing. Yu was appointed national secretary of the YMCA in 1913. When John R. Mott, the well-known leader of the student movement, came to China on a speaking tour in 1913, Yu served as one of his interpreters. In 1915 Yu was adviser and honorary secretary to the Chinese trade commission touring the United States.
In 1916 Yu was appointed acting general secretary of the YMCA. He soon succeeded C. T. Wang as general secretary and remained at the helm of the YMCA for 16 years. After being selected one of two "citizen representatives" by the Shanghai Chamber of Commerce and the National Federation of Educational Associations, he attended the Washington Conference in 1921. He encouraged the Chinese delegation to redeem the Shandong railway from the Japanese. He headed the fund-raising campaign that remitted the full sum to Japan in 1922.
Yu was elected chairman of the National Christian Council in 1922. He was also involved with the World Student Christian Federation. As a founding chairman of the Institute of Pacific Relations (IPR) in China, he led the Chinese delegation to the second IPR conference in Honolulu in 1927. He also attended the International Missionary Conference in Jerusalem in 1928.
After the Japanese invasion of Manchuria, Yu went on a special mission to the United States in 1932 to raise support for China. In 1933 he suffered a cerebral hemorrhage while in Washington for conferences with Secretary of State Henry L. Stimson. Yu returned to Shanghai and died in Jan 1936.
His best-known phrase, ren ge jiu guo (national salvation through the development of individual integrity), underlined his belief that the solution to national problems lay in the character of individuals. This resulted in his emphasis on the training of Chinese youths. He saw the YMCA as a means to strengthen and develop China. In the 1920s, he employed staff through the YMCA to tackle the problem of widespread illiteracy in China. Under his leadership, the YMCA provided moral guidance and made practical contributions toward China's progress.