We investigated femtosecond and picosecond time-resolved fluorescence dynamics of a tetrameric fluorescent protein Kaede with a red chromophore (red Kaede) to examine a relationship between the excited-state dynamics and a quaternary structure of the fluorescent protein. Red Kaede was obtained by photoconversion from green Kaede that was cloned from a stony coral Trachyphyllia geoffroyi. In common with other typical fluorescent proteins, a chromophore of red Kaede has two protonation states, the neutral and the anionic forms in equilibrium. Time-resolved fluorescence measurements clarified that excitation of the neutral form gives the anionic excited state with a time constant of 13 ps at pH 7.5. This conversion process was attributed to fluorescence resonance energy transfer (FRET) from the photoexcited neutral form to the ground-state anionic form that is located in an adjacent subunit in the tetramer. The time-resolved fluorescence data measured at different pH revealed that excited-state proton transfer (ESPT) also occurs with a time constant of 300 ps and hence that the FRET and ESPT take place simultaneously in the fluorescent protein as competing processes. The ESPT rate in red Kaede was significantly slower than the rate in Aequorea GFP, which highly likely arises from the different hydrogen bond network around the chromophore.