This paper considers agents＇ preference diversification and incorporates international goods trade into the Ramsey growth model of open economy. Agents not only consume domestic goods, but also import foreign goods for consumption. A sufficient condition is presented for the economy to exhibit the growth indeterminacy. If there exist the mild sector-specific externalities in the non-tradable sector and moreover the overall level of externalities in this sector is more than that of tradable goods sector, then the economic growth may own a continuum of trajectories converging to the sole balanced growth path （BGP） so that the economy exhibits local indeterminacy. In the meantime the economic calibrate with feasible parameter values is implemented and simulation results illustrate theoretical findings