The piezoelectric, ferromagnetism, and magnetoelectric response of BiFeO3–BaTiO3 ceramics with the compositions around the morphotropic phase boundary (MPB) of the solid solution are systematically investigated after the ceramics have been quenched from a high temperature. We find that the ferromagnetism of the quenched ceramics is greatly enhanced. An enhanced piezoelectric response d33 larger than 200 pC/N, which could be sustained up to 350 °C, is measured. As a result of enhanced ferromagnetism and piezoelectric response, a large magnetoelectric response ～ 1.3 V/cm·Oe (1 Oe = 79.5775 A·m-1) is obtained near the mechanical resonance frequency of the quenched ceramic samples. Our research also shows that in addition to the ferromagnetism and piezoelectric response, the mechanical quality factor is another important parameter to achieve high magnetoelectric response because the physical effects are coupled through mechanical interaction in BiFeO3-based materials. Our work suggests that quenching is an effective approach to enhancing the magnetoelectric response of BiFeO3-based materials and the materials belong to single-phase multiferroic materials with high magnetoelectric response.