In this paper,we consider the entanglement dynamics of a four-qubit model[2006 Phys.Rev.A 74 042328]where two entangled qubits a and b locally interact with separate qubits A and B via the spin-exchange-like Hamiltonian.We study the effect of purity of initial entangled state of qubits a,b on the entanglement evolution and its relation with energy transfer.Also,we find that the total bipartite entanglement of qubits a,b plus A,B is not a constant any longer when the initial entangled state of a,b is not pure,which is a complement to the result in the paper[2007 J.Phys.B 40 S45] for the pure case.