The crystallization kinetics of Cu47.5Zr47.5Al5 BMG was studied by differential scanning calorimetry (DSC) using the mode of continuous heating and isothermal annealing. It is found that Tg, Tx, and Tp, display a dependence on the heating rate in the case of continuous heating. The activation energies, Eg, Ex and Tp determined by the Kissinger method, yield 445, 264 and 285 kJ/mol, respectively. The local activation energy, E(x), was determined by the Doyle-Ozawa method, which gives the average activation energy 204 kJ/mol. On the other hand, the isothermal kinetics was modeled by the Johnson-Mehl-Avrami (JMA) equation, the Avrami exponent versus crystallization fraction was calculated at different temperatures. Details of nucleation and growth behaviors are discussed in terms of the local Avrami exponent and local activation energy during the isothermal crystallization. X-ray shows that the quenched BMG only includes the glass single phase. The BMG heated to 873 K has the precipitation of the body-center cubic (BCC) CuZr.