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A class of complex dynamical networks, in which the nodes have different state dimensions, is investigated in this paper. Since the networks constructed by nonidentical nodes with different state dimensions may exhibit different dynamical behavior, the appropriate control strategies are proposed for the stabilization and synchronization of such complex networks. By employing suitable controllers, sufficient conditions for finite-time stabilization and synchronization are derived based on the finite-time stability theory. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are presented to show the effectiveness of the proposed control methods.