A new set of color selection criteria (VJL) analogous with the BzK method is designed to select both star-forming galaxies (SFGs) and passively-evolving galaxies (PEGs) at 2.310^{10}M_{Sun}) galaxies at 2.30.4) SFGs, which however, only account for ~20% of the number density of massive SFGs. We also use the mid-infrared fluxes to clean our PEG sample, and find that galaxy size can be used as a secondary criterion to effectively eliminate the contamination of dusty SFGs. The redshift distribution of the cleaned PEG sample peaks at z~2.5. We find 6 PEG candidates at z>3 and discuss possible methods to distinguish them from dusty contamination. We conclude that at least part of our candidates are real PEGs at z~3, implying that this type of galaxies began to form their stars at z>5. We measure the integrated stellar mass density of PEGs at z~2.5 and set constraints on it at z>3. We find that the integrated stellar mass density grows by at least about factor of 10 in 1 Gyr at 3