Zr70Ni23Ti7 alloy contains a single amorphous phase when it is melt-spun at a wheel surface velocity over 20 m/s. The crystallization of these amorphous ribbons takes place through two exothermic reactions and shows a significant supercooled liquid region of about 30 K, indicating that the Zr70Ni23Ti7 alloy has a good glass-forming ability. The crystallization products of the first exothermic reaction for the ribbon prepared at a wheel surface velocity of 40 m/s are mainly an icosahedral quasicrystalline phase (I-phase) and some Zr2Ni phases. Further heating to a higher temperature will lead to the transformation of the metastable I-phase to Zr2Ni. Some icosahedral atomic clusters with a structure similar to those in face-centered-cubic Zr2Ni may exist in the alloy after rapid quenching, and most of them may act as nuclei of I-phase. The formation of I-phase in this alloy without any noble metals may be due to the proper atomic ratios in the system.