The effects of the Pr number on the countergradient scalar transfer in strong stable stratification are examined by means of a three-dimensional direct numerical simulation (DNS). A DNS based on a finite difference method is applied to unsheared thermally stratified water (Pr=5.0) and air (Pr=0.7) mixing layer flows downstream of turbulence-generation grids. The results show that the countergradient scalar transfer becomes significant in a thermally stratified water ow with a high P/ number and that the scale of Fluid motion which contributes to the countergradient scalar transfer is quite different between thermally stratified water and air flows. In a thermally stratified water ow small-scale motions first contribute to the countergradient scalar transfer, whereas in a thermally stratified air ow the small-scale countergradient transfer does not occur. The results agree well with previous laboratory measurements.