Ternary Ti61.2Cu32.5Fe6.3 quasiperitectic alloy is rapidly solidified in drop tube. The diameter of the obtained droplets varies from 80 to 1120 m. The theoretical analysis indicates that the range of undercooling is from 34 to 293 K (0.23TL). Due to the influences of containerless, microgravity, ultrahigh vacuum, etc, the microstructure of solidified alloy is composed of Cu0.8Fe0.2Ti phase, CuTi2 phase and CuTi3 phase. This result deviates appreciably from the equilibrium state. CuTi3 phase exhibits a conspicuous solute trapping effect during rapid solidification. The microstructure of alloy consists chiefly of eutectic (Cu0.8Fe0.2Ti and CuTi2 phases) and dendrites (Cu0.8Fe0.2Ti, CuTi3) structure. With the increase of undercooling, the microstructure of eutectic experiences a transition from strip eutectic cell to ellipsoidal eutectic cell to spherical eutectic cell; the morphology of Cu0.8Fe0.2Ti dendrite experiences a transition from coarse dendrites to broken dendrites to anomalous grain; while the morphology of CuTi3 dendrite changes from small block to coarse dendrite.