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We numerically investigate the effect of four kinds of partial attacks of multiple targets on the Barabási-Albert (BA) scale-free network and the Erd(o)s-Rényi (ER) random network.Comparing with the effect of single target complete knockout we find that partial attacks of multiple targets may produce an effect higher than the complete knockout of a single target on both BA scale-free network and ER random network.We also find that the BA ecale-free network seems to be more susceptible to multi-target partial attacks than the ER random network.