Constituent quark mass model is adopted as a tentative one to study the phase transition between two-flavour quark matter and more stable thres-flavour quark matter in the core of supernovae.The result shows that the transition has a significant influence on the increasing of the core temperature,the neutrino abundance and the neutrino energies,which contributes to the enhancement of the successful probability of supernova explosion.However,the equilibrium values of these parameters (except the temperature) from the constituent quark mass model in this work are slightly bigger than those obtained from the other model.And we find that the constituent quark mass model is also applicable to describing the transition in the supernova core.