In aqueous solution of 1,1'-diethyl-2,2'-carbocyanine J-aggregate, the exciton self-trapped (EST) state is usually expected to be negligible. However, in this work, by measuring transient absorption spectroscopy under a variety of excitation fluences, the EST state was found to be formed via coherent exciton-exciton annihilation (EEA), when the excitation fluence was high enough. With the existence of a shoulder-stimulated emission band at 615 nm and a broad EST state absorption band at long wavelength, diffusion-limited and coherent EEAs can be distinguished. Adaptive coherent control was employed to check if EEA dynamics can be influenced by a shaped excitation pulse. We found that both the diffusion-limited and coherent EEAs can be suppressed. Ground-state vibronic coupling and non-Condon-type exciton-phonon coupling were discussed to explain the observations.