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We investigate two classes of conditions for galaxy quenching at 0.5 ＜ z ＜ 2.5 based on the structural scaling relations of galaxies in the five Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey(CANDELS)fields:the formation of a compact core and the environment.We confirm that in the entire redshift range,massive quiescent galaxies(M ＞ 1010 M⊙)have much higher stellar mass surface densities within the central 1 kpc(∑1)and smaller sizes than star-forming galaxies in the same stellar mass range.In addition,the quiescent fractions significantly increase with the increase of ∑1 regardless of whether galaxies are centrals or satellites.In contrast,we find that the overall lower-mass quiescent galaxies(M* ＜～1O10M⊙)have slightly higher ∑1 and comparable sizes compared to star-forming galaxies of the same mass and at the same redshift.At z ＜ 1.5,satellites have higher halo masses and larger quiescent fractions than those of centrals at a given ∑1(stellar mass).Our findings indicate that the significant growth of the galaxy cores is closely related to the quenching of massive galaxies since z～2.5,while the environmental effect plays an important role in the quenching of low-mass galaxies at z＜1.5.