In light of recent developments in nearly AdS(2) holography, we revisit the semi-classical version of two-dimensional dilaton gravity proposed by Callan, Giddings, Harvey, and Strominger (CGHS) [1] in the early 90's. In distinction to the classical model, the quantum-corrected CGHS model has an AdS(2) vacuum with a constant dilaton. By turning on a non-normalizable mode of the Liouville field, i.e. the conformal mode of the 2d gravity, the explicit breaking of the scale invariance renders the AdS(2) vacuum nearly AdS(2). As a consequence, there emerges an effective one-dimensional Schwarzian-type theory of pseudo Nambu-Goldstone mode-the boundary graviton-on the boundary of the nearly AdS(2) space. We go beyond the linear order perturbation in non-normalizable fluctuations of the Liouville field and work up to the second order. As a main result of our analysis, we clarify the role of the boundary graviton in the holographic framework and show the Virasoro/Schwarzian correspondence, namely that the 2d bulk Virasoro constraints are equivalent to the graviton equation of motion of the 1d boundary theory, at least, on the SL(2, R) invariant vacuum.