This paper examines the role of immigrant networks on trade, particularly through the demand effect. First, we examine the effect of immigration on trade when the immigrants consume more of the goods that are abundant in their home country than the natives in a standard Heckscher-Ohlin model and find that the effect of immigration on trade is a priori indeterminate. Our econometric gravity model consists of 63 major trading and immigrant sending countries for the U.S. over 1991-2000. We find that the immigrants' income, mostly through the demand effect, has a significant negative effect on U.S. imports. However, if we include the effect of the immigrant income interacted with the size of the immigrant network, measured by the immigrant stock, we find that the higher the immigrant income the lower is the immigrant network effect for both U.S. exports and imports. This we find in addition to the immigrant stock elasticity of 0.27% for U.S. exports and 0.48% for U.S. imports. Capturing the immigrant assimilation with the level of immigrant income, this paper finds that the immigrant network effect on trade flows is weakened by the increasing level of immigrant assimilation.