The lead-free ferroelectric 0.5Ba(Zr0.2Ti0.8)O3 - 0.5(Ba0.7Ca0.3)TiO3 (BCZT) is a promising component for multifunctional multiferroics due to its excellent room temperature piezoelectric properties. Having a composition close to the polymorphic phase boundary between the orthorhombic and tetragonal phases, it deserves a case study for analysis of its potential for modern electronics applications. To obtain magnetoelectric coupling, the piezoelectric phase needs to be combined with a suitable magnetostrictive phase. In the current article, we report on the synthesis, dielectric, magnetic, and magnetoelectric characterization of a new magnetoelectric multiferroic composite consisting of BCZT as a piezoelectric phase and CoFe2O4 (CFO) as the magnetostrictive phase. We found that this material is multiferroic at room temperature and manifests a magnetoelectric effect larger than that of BaTiO3 -CoFe2O4 bulk composites with similar content of the ferrite phase.