Our previous work proposed that except for ferromagnetic and piezoelectric properties, mechanical quality factor is also an important parameter for high magnetoelectric response of BiFeO3-based multiferroic ceramics. In this work, in order to improve the mechanical quality factor of BiFeO3-based ceramics and obtain higher magnetoelectric response, we use Mn as a dopant and prepare 0.75BiFe(1-x)Mn(x)O(3)-0.25BaTiO(3) (x = 0, 0.0025, 0.005, 0.0075, 0.01) ceramics. The dielectric, piezoelectric, magnetic, and magnetoelectric properties of the ceramics with different Mn doping levels and different sintering temperatures are studied comprehensively. We find that the piezoelectric response, mechanical quality factor, ferromagnetic property, and magnetoelectric response can be improved by optimization of the composition and sintering temperature of the ceramics. A large magnetoelectric coefficient alpha(E) similar to 2 V/(cm Oe) is achieved at resonant frequency when doping content of Mn is 0.75 mol% and sintering temperature is 1030 degrees C. Such high value of alpha(E) is attributed to the combined effect of improved mechanical quality factor, high piezoelectric coefficient, and enhanced ferromagnetism. It is among the largest alpha(E) values obtained in single-phase BiFeO3-based ceramics. Moreover, our work further verifies the mechanical quality factor is an important parameter to achieve a high magnetoelectric response in BiFeO3-based ceramics.