Crystallization behavior of the Ti50Ni25Cu25 alloy was studied by means of scanning and isothermal differential calorimetry, X-ray diffraction, conventional and high-resolution transmission electron microscopy. A single stage polymorphic-type transformation of the amorphous phase forming a Ti2CuNi crystalline phase was observed. The activation energy for such a single stage crystallization of the amorphous phase was determined by Kissinger analysis. Kinetics of the crystallization was analyzed on the basis of Johnson-Mehl-Avrami equation and discussed regarding to the value of Avrami exponent obtained. Relatively high average value of Avrami exponent of 5.5 at the range from 702 to 709 K suggests nucleation with an increasing nucleation rate.