Zhou Shiming akakwikwidza mumakwikwi ake ekutanga emutambo wetsiva mumakwikwi eAsia Amateur Boxing Championships muna 2004 uye akahwina sirivheri, achirasikirwa mumutambo wekupedzisira naNoman Karim asi achikwikwidza kumitambo yeOlympic ya2004. Mumitambo yeOlympic yeZhizha ya2004, akakunda mutambo wake wekutanga nekurova Rau'shee Warren munharaunda ye32. Akarasikirwa nemukundi wekupedzisira Yan Bartelemí mumasemi-fainari uye akapedzisira akunda bronze. Zou akahwina 2005 World Amateur Boxing Championships nekukunda Pál Bedák mumutambo wekupedzisira, achiva mutambi wekutanga weChinese kuhwina mutambo uyu. PaMitambo yeAsia ya2006
, Zou akahwina goridhe nekukunda Suban Pannon 21-1 mumutambo wekupedzisira. Akadzokorora kukunda kwake kubva muna 2005 pa2007 World Amateur Boxing Championships, achirova David Ayrapetyan pakutanga kwemutambo uye Harry Tanamor mumutambo wekupedzisira; zvisinei, Zou aifanira kugutsikana nesirivha pa2007 Asian Amateur Boxing Championships, achirasikirwa mumutambo wekupedzisira naPürevdorjiin Serdamba.