Understanding of the correlation between the magnetomechancial coupling factors (k) and damping factors (Q^-1) is a key pathway to enhance the magnetomechanical power conversion ef-ficiency in laminated magnetoelectric (ME) composites by engineeringly manipulating the magnetic and mechanical properties of Fe-based amorphous metals. The k and Q^-1 factors of FeSiB amorphous ribbons annealed in air at different temperatures are investigated. It is found that k and Q^-1 factors are affected by both magnetic and elastic properties. The magnetic and elastic properties are equalized in terms of the magnetomechanical power efficiency for the low temperature annealing. The k and Q^-1 of FeSiB-based epoxied laminates with different stacking numbers show that the -3 dB bandwidth and Young’s modulus are equalized in terms of the magnetomechanical power efficiency for the high lamination stacking.