The magnetoelastic damping in magnetostrictive material is investigated. It is noted that the quality factor （the inverse measure of damping） of giant magnetostrictive material Terfenol-D is strongly dependent on bias direct current （DC） magnetic field. Taking advantage of the DC field dependence of magnetoelastic damping in magnetostrictive material, a DC or quasistatic magnetic sensor is proposed. The sensor is designed as a composite piezoelectric transformer （CPT） which is fabricated by bonding magnetostrictive material and piezoelectric transformer in layers. Theoretical analysis shows that the output voltage of the CPT is directly proportional to the quality factor of the CPT. Therefore, the output voltage of the CPT also strongly depends on DC field due to the strong field dependence effect of quality factor in magnetostrictive material. In addition, the ΔE effect of magnetostrictive material has little influence on the magnitude of the output voltage. A Terfenol-D/PZT8 composite transformer is fabricated for experiment. The experimental results show that the output sensitivity to DC field achieves ~5.12 mV·Oe-1 when the CPT is driven near resonance by an AC voltage with amplitude of 0.5 V.