The present study reports the numerical simulation of turbulent plane offset jet flow over a moving plate. The effect of plate velocity on various flow characteristics is discussed in detail including the special case of a stationary plate. For turbulence closure, the low-Reynolds number (LRN) turbulence model proposed by Yang and Shih (YS) is applied because it is computationally robust and reported to work quite effectively in several complex flow situations. The computations have been carried out with a Reynolds number of 15,000 for various offset ratios (OR = 3, 7, and 11) and different velocity ratios (Uplate) of the plate in the range 0–2. The finite volume method (FVM) with a staggered grid arrangement has been used to solve the transport equations. The application of the LRN model along with the integration to wall (ITW) approach enables us to capture one closed loop of the Moffatt vortex near the left corner of the wall for the stationary plate case. The spreading of the jet has been found to reduce by increasing the velocity of the plate. The jet half-width lies very close to the wall for the plate to jet velocity 1.5 and 2. For two extreme limits of plate velocity, i.e., Uplate = 0 and 2, the nearly self-similar profiles are observed at different axial locations in the wall jet region. Also, the flow is observed to exhibit nearly self-similar behavior when velocity profiles are plotted for various offset ratios at a given axial location in the wall jet region for Uplate = 0 and 2. It has been found that the flow characteristics are significantly influenced by the plate velocity.