Based on constituent quark mass and current quark mass model, the phase transition of two-flavor quark matter to more stable three-flavor quark matter in the core of supernova is studied. It is shown that the timescale of the process is shorter than 10-8 seconds for both cases, and the smaller the quark mass (current quark mass), the quicker the process; and the equilibrium parameters, except the temperature, such as s-quark abundance, neutrino abundance and total neutrino energy in supernova core, have a slight increase compared to the former result after the conversion according to constituent quark mass model. But the values of those parameters (including temperature) increase significantly based on current quark mass model. The current quark mass will be more favorable for the success of the delayed neutrino-heating mechanism for the explosion.