Using a stellar mass-limited sample of ∼46,600 galaxies (M M 10 9.1 * > ) at z 0.5 2 < < , we show that the stellar mass, rather than the environment, is the main parameter controlling quenching of star formation in galaxies with M M 10 10 * > out to z = 2. On the other hand, the environmental quenching becomes efficient at z 1 < regardless of galaxy mass, and it serves as a main mechanismfor quenching star formation for lower mass galaxies. Our result is based on deep optical and near-infrared imaging data over 2800 arcmin 2 , enabling us to negate cosmic variance and identify 46 galaxy cluster candidates with M M 10 14 . From M 10 9.5 *~t o M 10 10.5 , the fraction of quiescent galaxies increases by a factor of ∼10 over the entire redshift range, but the difference between cluster and field environment is negligible. Rapid evolution in the quiescent fraction is seen from z = 2 to z = 1.3 for massive galaxies, suggesting a build-up of massive quiescent galaxies at z 1.3 > . For galaxies with M M 10 10 * < at z 1.0 < , the quiescent fraction is found to be as much as a factor of 2 larger in clusters than in field, showing the importance of environmental quenching in low-mass galaxies at low redshift. Most high-mass galaxies are already quenched at z 1 > , therefore environmental quenching does not play a significant role for them, although the efficiency of environmental quenching is nearly identical between high-and low-mass galaxies.