The isothermal crystallization behaviors in a newly developed CeGaCu bulk metallic glass have been investigated through the classic differential scanning calorimeter (DSC) method. It is found that the apparent activation energy (Ea) strongly depends on the fraction (x) of isothermal crystallization. Johnson-Mehl-Avrami (JMA) formula was used to analyze the mechanism of crystallization and the obtained Avrami exponent (n) was discovered to show an obvious correlation with the crystallization fraction x. With the help of the relation between Ea and n, the nucleation and growth activation energies, En and Eg, were estimated to be 214-304 kJ/mol and 91 kJ/mol, respectively. This result suggests that the main energy barrier against crystallization in the present glass should be the nucleation of nucleates, rather than the growth of crystals. Such a large E, is also believed to be responsible for the good glass forming ability of the CeGaCu alloy.