Magnetoelectric composites enjoy large magnetoelectric transfer efficiency at resonance frequency, accompanying a large phase shift. We prepared two magnetoelectric laminate composites to research the origin of large phase shift and magnetoelectric characteristics by electric-field-induced strain and magnetic-field-induced strain. The piezoelectric part plays a dominant role in both the direct and converse magnetoelectric resonances. The electromechanical resonance inspires direct and converse magnetoelectric resonant peaks, and results in the magnetoelectric phase shift of near π around the resonance frequency. However, the magnetostrictive part is difficult to inspire the magnetoelectric resonance and phase shift.