A new k-epsilon model which includes damping effect on vertical turbulent transport due to thermal stratification is proposed. The proposed model was tested by application to two kinds of two-dimensional thermally stratified flow fields. One is a high-Reynolds-number open channel flow, and the other is a low-Reynolds-number flowfield within an enclosure. The new model also includes low-Reynolds-number treatment which is effective not only in the vicinity of the wall, but also apart from the wall. With the aid of this new low-Reynolds-number treatment, the proposed k-epsilon model becomes applicable to a flowfield which includes both turbulent area and pseudo-laminar area caused by thermal stratification. The agreement between the results given from the new k-epsilon model and the experimental results was rather good.