A non-isothermal phase-field model is used to simulate the rapid solidification of highly undercooled alloy melts.The influence of undercooling on the solidification process is studied. It is indicated that with the increase of undercooling, the dendrite morphology changes from poorly developed dendrite, via the well-developed dendrite containing secondary and teary arms, to the compact diamond-shaped grain. With increasing undercooling, the tip radius changes in the following rule: decrease → increase → decrease while the growth velocity increases constantly, which is consistent with the results predicted by the Boettinger-Coriell-Trivedi model. The thermal, solutal and kinetic undercooling contributions under different initial undercooling are also determined. It is shown that when the undercooling is increased beyond a certain value, the thermal undercooling contribution exceeds the solutal contribution and the dendrite growth transits from solutal diffusion controlled to thermal diffusion controlled one.