The effect of trade quotas on firms’ incentive to invest in cost-reducing R&D is studied in a two-stage price-setting duopoly game. A domestic and a foreign firm first choose R&D levels and then set the prices of their differentiated products in the domestic market. With a quota imposed at, or close to, the free-trade level of imports, the domestic firm faces less competition than under free-trade and invests less in R&D. Contrarily, the constrained foreign firm invests more in R&D as the negative strategic effect of a reduction in its cost is now absent. These results differ partially from the Cournot duopoly case in which R&D expenditures are lower for both the firms. As the quota becomes more restrictive, the domestic firm increases and the foreign firm decreases its expenditures on R&D. Domestic welfare is always higher under free-trade than under any quota regardless of the degree of product substitutability.