  In this letter, we use a two-color (J-L) vs. (V-J) selection criteria to
search massive, quiescent galaxy candidates at 2.5<z<4.0 in the CANDELS-COSMOS
field. We construct a H-selected catalogue and complement it with public
auxiliary data. We finally obtain 19 passive VJL-selected (hereafter pVJL)
galaxies as the possible massive quiescent galaxy candidates at z~3 by several
constrains. We find the sizes of our pVJL galaxies are on average 3-4 times
smaller than those of local ETGs with analogous stellar mass. The compact size
of these z~3 galaxies can be modelled by assuming their formation at z ~ 4-6
according to the dissipative collapse of baryons. Up to z<4, the
mass-normalized size evolution can be described by $r_e\propto (1+z)^{-1.0}$.
Low Sersic index and axis ratio, with median values n~1.5 and b/a~0.65
respectively, indicate most of pVJL galaxies are disk-dominated. Despite large
uncertainty, the inner region of the median mass profile of our pVJL galaxies
is similar to those of quiescent galaxies (QGs) at 0.5<z<2.5 and local
Early-type galaxies (ETGs). It indicates local massive ETGs have been formed
according to an inside-out scenario: the compact galaxies at high redshift make
up the cores of local massive ETGs and then build up the outskirts according to
dissipationless minor mergers.
