An excited-state intramolecular proton transfer (ESIPT) reaction of 4'-N,N-dimethylamino-3-hydroxyflavone in room temperature ionic liquid is theoretically investigated using RISM-SCF-SEDD, which is a hybrid method of molecular liquid theory and ab initio molecular orbital theory. The photo-excitation and proton-transfer processes are computed by considering the solvent fluctuation. The calculated absorption and emission energy are in good agreement with the experiments. The changes in the dipole moment indicate that the drastic solvation relaxation is accompanied by the excitation and an ESIPT process, which is consistent with the remarkable dynamic Stokes shift observed in the experiments. We calculated the nonequilibrium free-energy contour as a function of the proton coordinate and the solvation coordinate. We conclude that although immediately after the excitation the barrier height of the ESIPT process is relatively small, the barrier becomes larger as the solvation relaxation to the excited normal state proceeds. The solvation relaxation process is also investigated on the basis of microscopic solvation structure obtained by RISM calculations.