Magnetoelectric studies on BaTi 1−x Sn x O 3 /NiFe 2 O 4 (x = 0.07, 0.08, 0.09 and 0.10) lead-free bilayer laminated composites were investigated at 1 kHz and resonance frequencies. The pure phase formation of BaTi 1−x Sn x O 3 and NiFe 2 O 4 samples was confirmed by X-ray diffraction technique. The ferroelectric BaTi 1−x Sn x O 3 layers of different compositions having large piezocoefficient were used for the ME studies. The composites displayed their maximum magnetoelectric voltage coefficient at resonance peaks related to the 1st radial mode. The thickness dependent magnetoelectric studies on composites with x = 0.08 revealed a giant magnetoelectric voltage coefficient of 24.53 V cm −1 Oe −1 at 285 kHz under bias field condition. Remarkably, a large self-biased magnetoelectric response of the order of ~ 2–5 V cm −1 Oe −1 at resonance was exhibited by the composites. The observed large and self-biased magnetoelectric response in BaTi 1−x Sn x O 3 /NiFe 2 O 4 composites enables them to be a useful lead-free alternative for several magnetoelectric related applications. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.