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We study entanglement properties of the three-qubit anisotropic Heisenberg model with both uniform and nonuniform exteal magnetic fields. Analytic expressions for the measures of entanglement at the ground state are obtained. We show that the pairwise entanglement and global entanglement of the system at the ground state clearly depend on the strength and configuration of exteal fields. The entanglement between some pairs can be enhanced by non-uniform exteal fields.