Amorphous Ti-(50-x)Ni-xCu (at%) (x = 20, 25, 27, 30) alloy ribbons were prepared by melt spinning. Subsequently, the crystallization behavior of the alloy ribbons was investigated by X-ray diffraction and differential scanning calorimetry. ${Delta}T$ (the temperature gap between $T_g$ and $T_x$) increased from 33 K to 47 K and the wavenumber ($Q_p$) decreased from 29.44 $nm^{-1}$ to 29.29 $nm^{-1}$ with increasing Cu content from 20 at% to 30 at%. The activation energy for crystallization decreased from 188.5 kJ/mol to 170.6 kJ/mol with increasing Cu content from 20 at% to 25 at%; afterwards, the activation energy remained near constant. Crystallization occurred in two-stage: amorphous-B2-$TiCu_2$ in Ti-Ni-Cu alloys with Cu content less than 25 at%, while it occurred in three-stage; amorphous-B2-TiCu-$TiCu_2$ in Ti-Ni-Cu alloys with Cu content more than 27 at%.