Using a commercially available anisotropic magnetoresistance (AMR) sensor of HMC1001, we developed a sensitive magnetometer. It could operate in amplifier mode or feedback mode. The magnetic field sensitivity of the AMR sensor was about 3.2 mV/V G. When the AMR sensor was biased by a voltage of 24 V, the magnetic field resolutions of the AMR magnetometer were about 12 pT/square root(Hz) at 1 kHz and 20 pT/square root(Hz) at 100 Hz. We used the AMR magnetometer for Eddy-current nondestructive evaluation in unshielded environment.