As the traditional strategic trade policies are restricted by WTO，green subsidy，as a strategy with environmental policy effect，is adopted by many countries．In a multi-stage duopoly competition model，this paper investigates the mechanism of green subsidy and its spillover effect on government and firm behaviors．The results show that if the government provides unilateral green subsidies to domestic firms in accordance with the EOS and SOS respectively，only the subsidy under SOS can improve domestic social welfare by changing firms’Cournot output and environmental emission standard．However，compared with EOS，the green subsidy under SOS may give the government a stronger incentive for ecological dumping，which makes the domestic environment more likely to deteriorate．In addition，owing to technology spillover，the domestic welfare declines as its emission standard raises and firms profit reduces，while the foreign welfare improves as both their emission standards and firms’profits increase．In a generalized model，it is found that the government’s rational environmental policy is to offer the optimal green subsidies in non-cooperative cases or levy the optimal taxes in cooperative cases．