Compared with Ti41Zr25Be28Fe6 bulk metallic glass, (Ti41Zr25Be28Fe6)93Cu7 glassy alloy possesses a much narrower supercooled liquid region but the glass-forming ability is dramatically improved. Isochronal and isothermal differential scanning calorimetry measurements were adopted to investigate Cu-alloying effect on the crystallization transformation kinetics of Ti41Zr25Be28Fe6 glassy alloy. It is found that Cu alloying increases the activation energies of Ti41Zr25Be28Fe6 glassy alloy for glass transition and crystallization in continuous heating. Moreover, the isothermal activation energy of (Ti41Zr25Be28Fe6)93Cu7 glassy alloy increases as process of crystallization transformation, while Cu-free alloy exhibits a contrary tendency. The addition of Cu also decreases the Avrami exponent of the base alloy, resulting in the suppression of crystal nucleation and growth.