The evolutionary tracks of a protostar of one solar mass under quasi-hydrostatic equilibrium are computed with mass-accretion time scales of $10^3,;10^4,;10^5;and;10^6$ years, and their resulting behaviors in the H-R diagram are discussed. It is found that there exists a critical time scale of mass accretion, which reverses the course of their evolutionary tracks. A value of the critical time scale appears to lie between $10^3;and;10^4$ years. The physical cause for the presence of the critical time scale is discussed. Finally, it is proposed that star formation requires at least several $10^3$ years before any star is born out of dark dense interstellar clouds.