A seeing model based on the Tatarskii equation, which uses wind shear and temperature gradient as inputs, has been proposed for Dome A in our previous study. It has been shown that the seeing was correctly reproduced statistically. In this paper, in order to investigate the ability of the Polar version of the Weather Research and Forecasting (PWRF) model to forecast the seeing, we have tried three different PWRF-simulated wind shear and temperature gradient combinations of two levels for the near-ground. The three combinations all give good performance with the correlation coefficients being higher than 0.75, when compared with the seeing measured by the Kunlun Differential Image Motion Monitor at Dome A during the summer of 2019. Besides this, the gradient Richardson number (Ri), which was also simulated by the PWRF model, basically behaved as expected as the Ri is generally large when the measured seeing is small. These results suggest that the PWRF model can be used to forecast the astronomical seeing above Dome A.