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In this paper, we first present a scheme for teleporting an unknown four-qubit cluster state via a cluster state chain between two distant nodes, which do not share entanglement pairs directly. Adjacent nodes are linked by a partially entangled four-qubit cluster state with each other. In our scheme, we deduce the relationship between the coefficients of the entangled cluster states and the success probability of teleportation. Moreover, we derive the unitary matrixes for establishing direct channel between two distant nodes, which reduce the computational complexity and resource consumption significantly. By performing entanglement swapping simultaneously, our scheme is more flexible and efficient than most existing schemes.