The dynamic magnetostriction characteristics of an Fe-based nanocrystalline FeCuNbSiB alloy are investigated as a function of the dc bias magnetic field. The experimental results show that the piezomagnetic coefficient of FeCuNbSiB is about 2.1 times higher than that of Terfenol-D at the low dc magnetic bias $H_{dc}$ = 46 Oe. Moreover, FeCuNbSiB has a large resonant dynamic strain coefficient at quite low Hdc due to a high mechanical quality factor, which is 3-5 times greater than that of Terfenol-D at the same low $H_{dc}$. Based on such magnetostriction characteristics, we fabricate a new type of transducer with FeCuNbSiB/PZT-8/FeCuNbSiB. Its maximum resonant magnetoelectric voltage coefficient achieves ~10 V/Oe. The ME output power reaches 331.8 ${mu}W$ at an optimum load resistance of 7 $k{Omega}$ under 0.4 Oe ac magnetic field, which is 50 times higher than that of the previous ultrasonic-horn-substrate composite transducer and it decreases the size by nearly 86%. The performance indicate that the FeCuNbSiB/PZT-8/FeCuNbSiB transducer is promising for application in highly efficient magnetoelectric energy conversion.