We examine the trade policy effects on the quality and composition of imports in an oligopolistically competitive market. Foreign producers compete in quantity as well as in quality of outputs. We show that consumer exclusions always occur due to the trade policy and prove that a specific tariff upgrades the quality choice of some consumers who purchased the minimum quality requirement's quality level. However, the specific tariff does not affect the quality choice of the remaining consumers who purchased at a quality level higher than the minimum quality requirement (MQR). Under some conditions, an ad valorem tariff is shown to downgrade the quality of imports. Furthermore, a quota is also proved to downgrade the quality of imports, to lower the social welfare, and to raise the prices of imports. Moreover, we also investigate a policy with a quality ceiling on imports. In this regime we demonstrate that a specific tariff downgrades the quality choice of some consumers who purchased the maximum quality level. Finally, we derive the condition and demonstrate that an increase in the MQR results in a smaller market size and upgrades the quality of imports.