The implications of trend inflation in an open economy are investigated in a two-country DSGE model. The results show that increasing trend inflation from 2 to 4 percent in the domestic country generates a consumption-equivalent welfare loss of about 0.36 percent and 0.04 percent in the domestic and foreign countries, respectively. The cooperative optimal monetary policy under commitment with positive trend inflation faces a policy trade-off in response to technology shocks. Incorporating trend inflation in an open economy has new dynamics: domestic trend inflation amplifies the spillover effects of a domestic technology shock on foreign countries; trend inflation in foreign countries reinforces these spillover effects through the effect of price dispersion.