We demonstrate theoretically a scheme for cluster-state generation, based on atomic ensembles and the dipole-blockade mechanism. In the protocol, atomic ensembles serve as single-qubit systems. Therefore, we review single-qubit operations on qubit defined as collective states of atomic ensemble. Our entangling protocol requires nearly identical single-photon sources, one ultracold ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates in a single step Q-qubit GHZ states with success probability p_success~?^Q/2, where ? is the combined detection and source efficiency. This is significantly more efficient than any known robust probabilistic entangling operation. GHZ states form the basic building block for universal cluster states, a resource for the one-way quantum computer.