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We have studied the aggregation of particles on a hetero-suhstrate consisting of two different substrates A and B with finite surface barriers EAB and EBA between the AB and BA boundaries, respectively. With the diffusion energy limited aggregation (DELA) model, we find that the number of clusters and the mean radius of gyration of the clusters are dependent on the surface barriers EAB and EBA. For the case with a constant of EBA, a series of minima are summarized as EAB = (E0 - kBAEBA)/kAB with kAB and kBA being two integers, for main minima (kBA = kAB - 1) and two local minima (kBA = kAB and kBA = kAB + 1) between two neighbouring main minima.