Su became a popular teen idol in the 1980s as a member of the boyband Xiao Hu Dui. He was known as the "Obedient Tiger" (乖乖虎) until the band broke up in 1995.

The 1998–1999 hit TV series My Fair Princess marked a turning point in Su's career. Since then he has had a successful career in acting, starring in highly popular dramas such as The Legendary Siblings (1999), Romance in the Rain (2001), and The Heaven Sword and Dragon Saber (2003). Su has won awards from Hundred Flowers Awards and Macau International Movie Festival for the films The Message (2009) and The Love Song of Kang Ding (2010) respectively.

In 2013 he produced the TV series Destiny by Love. In 2015 he directed the film The Left Ear.

Alec Su's career started in 1988, at the age of 15, when he joined the Little Tigers trio. The band was the first idol singing group that debuted in the Taiwanese music industry and Alec was labelled as the "obedient tiger." The group's popularity was unprecedented; the Little Tigers attracted fans from Taiwan, Hong Kong, China, Singapore, and amongst Chinese communities around the world. The success of the band began the new generation of Taiwanese pop culture in the early 1990s. In 2010, the Little Tigers were invited to participate in the CCTV Spring Festival Gala, in which they sang a medley of three of their biggest hits and won accolades as the "favorite singing group" for the event.

Apart from being a popular singer, during this period Su was epitomized by the general public as a superior student. He attended Taiwan's number one high school, Taipei Municipal Jianguo High School and was accepted into the prestigious National Taiwan University, where he majored in Mechanical Engineering . Su's experiences describing his high school years, preparing for the Taiwan university entrance examinations while trying to also juggle his performing schedule as a member of a wildly popular singing group, are recorded in his 1995 book entitled My Days at Jian Zhong / Youth Never Die.

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