Most studies on parallel trade conclude that parallel imports, in general, benefit the importing country because it lowers the price of parallel imports and benefits to the consumers in the importing country. Richardson [1] explicitly indicates that there is no importing country not to permit parallel imports because they are discriminated against in its absence. However, an obvious counter example is observed in the US. In this paper, we propose a two-country model of parallel trade with innovation to explain why some countries, such as the US would like to prevent parallel imports. We show that the elasticity of innovation is crucial to the welfare of importing country and global welfare.