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Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the self-diffusion dynamics properties of palladium atomic clusters up to seven atoms on the Pd (1 1 1) surface have been studied at temperatures ranging from 300 to 1000 K. The simulation time varies from 20 to 75 ns according to the cluster sizes and the temperature ranges. The heptamer and trimer are more stable than the other neighboring clusters. The diffusion coefficients of the clusters are derived from the mean square displacement of the cluster's mass-center, and the diffusion prefactors D0 and activation energies Ea are derived from the Arrhenius relation. The activation energy of the clusters increases with the increasing atom number in the clusters, especially for Pd6 to Pd7. The analysis of trajectories shows the noncompact clusters diffuse by the local diffusion mechanism but the compact clusters diffuse mainly by the whole gliding mechanism, and some static energy barriers of the diffusion modes are calculated. From Pd2 to Pd6, the prefactors are in the range of the standard value 10−3 cm2 s−1, and the prefactor of Pd7 cluster is 2 orders of magnitude greater than that of the single Pd adatom because of a large number of nonequivalent diffusion processes. The heptamer can be the nucleus in the room temperature range according to nucleation theory.