We investigate peculiar velocities predicted for clusters in Lambda cold dark matter ($Lambda$CDM) models assuming that the initial density fluctuation field is Gaussian. To study the non-linear regime, we use N-body simulations. We investigate the rms velocity and the probability distribution function of cluster peculiar velocities for different cluster masses. To identify clusters in the simulation we use two methods: the standard friends-of-friends (FOF) method and the method, where the clusters are defined as maxima of a smoothed density field (DMAX). The density field is smoothed with a top-hat window, using the smoothing radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc. The peculiar velocity of the DMAX clusters is defined to be the mean peculiar velocity of matter within a sphere of the radius $R_s$. We find that the rms velocity of the FOF clusters decreases as the cluster mass increases. The rms velocity of the DMAX clusters is almost independent of the cluster mass and is well approximated by the linear rms peculiar velocity smoothed at the radius $R=R_s$. The velocity distribution function of the DMAX clusters is similar to a Gaussian.
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