  The fidelity and entropy in an easy-axis antiferromagnetic Heisenberg spin-1
chain are studied numerically. By using the method of density-matrix
renormalization group, the effects of anisotropy on fidelity and entanglement
entropy are investigated. Their relations with quantum phase transition are
analyzed. It is found that the quantum phase transition from the Haldane spin
liquid to N\'eel spin solid can be well characterized by the fidelity. The
phase transition can be hardly detected by the entropy but it can be
successfully detected by the first deviation of the entropy.
