The CVB3LYP functional, which has been developed for evaluating both core and valence excitation energies with high accuracy, is applied to real-time time-dependent density functional theory (RT-TDDFT) calculations. The core excitation energies from the Is orbitals of several second-row atoms obtained by RT-TDDFT with the CVB3LYP functional were demonstrated and compared with those of the frequency-domain TDDFT.