Quenching is a key topic in exploring the formation and evolution of galaxies. In this work, we study the quenching rate, i.e., the variation in the fraction of quenched galaxies per unit time, of the Illustris-1 simulation. By building the quenched fraction function $f(m,rho, t)$ of each snapshot in the simulation, we derive an accurate form of quenching rate as $Re_q=df(m,rho,t)/dt$. According to the analytic expression of the quenching rate $Re_q$, we split it into four components: mass quenching, environmental quenching, intrinsic mass quenching and intrinsic environmental quenching. The precise value and evolutions can be given via the formula of $Re_q$. With this method, we analyze the Illustris-1 simulation. We find that quenched galaxies concentrate around $M_*simeq10^{11}h^{-1}M_odot$ and $delta+1simeq10^{3.5}$ at earlier times, and that the quenching galaxy population slowly shifts to lower stellar mass and lower overdensity regions with time. We also find that mass quenching dominates the quenching process in this simulation, in agreement with some previous analytical models. Intrinsic quenching is the second most important component. Environmental quenching is very weak, because it is possible that the pre- or postprocessing of environments disguises environmental quenching as intrinsic quenching. We find that our method roughly predict the actual quenching rate. It could well predict the actual amount of galaxies quenched by intrinsic quenching. However, it overestimates the amount of mass quenching galaxies and underestimates the amount of environmental quenching. We suggest that the reason is the nonlinearity of the environmental overdensity change and mass growth of the galaxy.
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