In this paper, we investigate the resonance magnetoelectric (ME) effect in the middle supported multilayer composites consisting of high-permeability Fe-based nanocrystalline soft magnetic alloy Fe73.5Cu1Nb3Si13.5B9 (FeCuNbSiB), Nickel (Ni), and piezoelectric Pb(Zr1-x Ti (x) )O-3 (PZT). The coupling effect between positive magnetostrictive FeCuNbSiB and negative magnetostrictive Ni results in the build-in magnetic bias due to their different magnetic permeability and coercivity. As a result, a giant resonance ME voltage coefficient (alpha (ME,r) ) at zero DC magnetic bias field (H (dc)) and multi-peaks of alpha (ME,r) for FeCuNbSiB/Ni/PZT/Ni/FeCuNbSiB composite are observed. The experimental results show that the giant zero-biased alpha (ME,r) strongly depends on the thickness of FeCuNbSiB ribbon. The maximum zero-biased alpha (ME,r) is up to 86 V/cm Oe for FeCuNbSiB/Ni/PZT/Ni/FeCuNbSiB with four-layer FeCuNbSiB ribbons, which is similar to 500 times higher than that of the previously reported NKNLS-NZF/Ni/NKNLS-NZF trilayer composite. Compared with the peak alpha (ME,r) and the optimum H (dc) of Ni/PZT/Ni composite, the largest peak alpha (ME,r) of FeCuNbSiB/Ni/PZT/Ni/FeCuNbSiB composite with four-layer FeCuNbSiB ribbons increases similar to 185 %, and the optimum H (dc) decreases similar to 300 Oe, respectively. Based on the nonlinear magnetostrictive constitutive relation and the magnetoelectric equivalent circuit, a theoretical model of alpha (ME,r) versus H (dc) is built under free boundary conditions. Calculated zero-biased alpha (ME,r) and alpha (ME,r) versus H (dc) are in good agreement with the experimental data. This laminate composite shows promising applications for high-sensitivity power-free magnetic field sensors, zero-biased ME transducers and small-size energy harvesters.