This paper examines the optimal trade and privatization policies in an international mixed market where a domestic public firm competes against domestic and foreign private firms. We consider a trade policy combination of production subsidy and import tariff, and compare the optimal trade and privatization policies under either Cournot or Stackelberg competition. We find that the optimal trade policies consist of a domestic production subsidy and an import tariff, which are identical under the two regimes regardless of the competition pattern. However, the optimal privatization policy depends on the competition patterns, whether Cournot or Stackelberg competition. In particular, the optimal privatization policy under Cournot competition is complete privatization, whereas that under Stackelberg competition is full nationalization. Finally, we show that if the government can only use a single trade policy instrument, the production subsidy gives a better social welfare benefit than the import tariff.