We report low-temperature dynamic properties of the quantum one-dimensional antiferromagnetic Heisenberg model with spin S=1. The dynamic correlation function is calculated using a procedure that combines a projection operator technique proposed by Reiter and a modified spin wave theory proposed by Takahashi. This modified spin wave theory predicts a temperature-dependent gap whose behavior is compared to the behavior obtained experimentally and also from different approaches. Our calculation suggests that the gap has strong effects on the shape of the dynamical correlation function.