  We study how primordial non-Gaussianity affects the pairwise velocity
probability density function (PDF) using an analytical model and cosmological
N-body simulations. We adopt the local type non-Gaussian models characterized
by f_{nl}, and examine both the linear velocity difference PDF and the linear
pairwise velocity PDF. We show explicitly how f_{nl} induces correlations
between originally independent velocities along the parallel and the
perpendicular to the line of separation directions. We compare the model
results with measurements from N-body simulations of the non-Gaussian models.
Linear theory fails to predict the PDF in the f_{nl} models. Therefore we
develop an analytic model based on the Zeldovich approximation to describe the
evolution of the velocity PDF. Our analytical model and simulation results show
remarkably good agreement in both the parallel and the perpendicular directions
for the PDF profiles, as well as the change in the PDF due to primordial
non-Gaussianity. The agreement is particularly good for relatively small
separations (< 10 h^{-1} Mpc). The inclusion of the evolution of the velocity
PDF is important to obtain a good description on the signature of primordial
non-Gaussianity in the PDF. Our model provides the foundation to constrain
f_{nl} using the peculiar velocity in future surveys.
