Kammala jumla mai zuwa: Zou Shiming ya fafata a gasar dambe mai sonsa ta farko a Gasar dambe mai son Asiya ta 2004 kuma ya lashe azurfa, inda ya yi rashin nasara a wasan karshe da Noman Karim amma ya cancanci shiga wasannin Olympics na bazara na 2004. A Wasannin Olympics na bazara na 2004, ya ci wasan farko ta hanyar doke Rau'shee Warren a zagaye na 32. Ya yi rashin nasara a kan zakara Yan Bartelemí a wasan kusa da na karshe kuma ya gama lashe tagulla. Zou ya lashe gasar zakarun duniya ta 'yan wasan dambe ta 2005 ta hanyar doke Pál Bedák a wasan karshe, ya zama dan damben kasar Sin na farko da ya lashe gasar. A cikin
Wasannin Asiya na 2006, Zou ya lashe zinare ta hanyar doke Suban Pannon 21-1 a wasan karshe. Ya maimaita nasararsa daga 2005 a gasar zakarun duniya na 'yan wasan tsere na 2007, inda ya doke David Ayrapetyan a farkon gasar da Harry Tanamor a wasan karshe; duk da haka, dole ne Zou ya gamsu da azurfa a gasar zakarun Asiya ta 2007, inda ya yi rashin nasara a wasan karshe da Pürevdorjiin Serdamba.