He hailed from Duling 杜陵 (near modern Xi'an 西安, Shaanxi). His father Su Jian 蘇建 had been an officer of general Wei Qing 衛青 who had fought against the steppe federation of the Xiongnu 匈奴 and was later governor (taishou 太守) of the commandery of Dai 代. Su Wu was an attendant (lang 郎) in his father's staff and was soon promoted to overseer of the imperial stables (chizhong jiujian 栘中廄監).
In 100 BCE he was appointed Leader of Court Gentlemen (zhonglangjiang 中郎將) and entrusted with a diplomatic mission to the Xiongnu, involving the exchange of hostages. A minor khan (wang 王 "prince") called Gou 緱 planned to rebel against Khan (chanyu 單于) Qietihou 且鞮侯 and to ally with the Han empire, and secretly plotted with some persons of Su Wu's entourage. When the plot was reveiled, Su Wu tried to commit suicide because he was the responsible ambassador. The khan had arrested Su Wu and kept him prisoner in a cave. Although he was not given food, Su Wu refused to submit to the Xiongnu. Even when he was transported to north of the steppe, Su Wu preferred to live a life of a shepherd and smashed his seal rather than to hand it over to the Xiongnu.
Only in 87 BCE, when Emperor Zhao 漢昭帝 (r. 87-74 BCE) mounted the throne, an "alliance by marriage" (heqin 和親) between the Xiongnu and the Han empire was concluded, and Su Wu was required to return to China. Yet the khan refused to send him back under the pretext that he was already dead. Years later an envoy of the Han court found out that he and his men were still alive. A story was invented that the emperor had during a hunt shot a goose at whose foots a letter was tied written by Su Wu. This trick succeeded, and the khan released Su Wu and his staff.
They returned to the capital Chang'an 長安 (modern Xi'an) after having spent 19 years among the Xiongnu. For this hard endurance Su Wu was appointed Supervisor of Dependent Countries (dianshuguo 典屬國).