This paper considers the mixed duopoly market competition where both public and private firms produce outputs and emit pollutions in the two separated markets, and examine the effect of trans-boundary externality on the relationship between privatization and environmental tax. The followings are the main results of our analysis. First, when the level of environmental tax is low, full privatization would be a policy alternative to maximize the social environmental welfare. But, when the level of environmental tax is high, full privatization should not be chosen for the social environmental welfare. Second, when trans-boundary externality is weak, partial privatization would be a policy alternative to maximize the social environmental welfare. But, when trans-boundary externality is strong, full privatization might be chosen for the social environmental welfare. Finally, when the level of environmental tax is low or trans-boundary externality is strong, privatization policy would be a complementary to environmental policy. But, when the level of environmental tax is high or trans-boundary externality is weak, privatization policy would be a substitute to environmental policy.