Broadband real-time dynamic vibronic coupling in Chl-a were experimentally studied using few cycle laser pulses of 6.8fs duration and a 128-channnel lock-in amplifier. Thanks to the extreme temporal resolution benefitting from the ultrashort laser pulse, the real-time modulation of the electronic transition energy induced by the molecular vibrations were calculated by the time dependent first moments of the bleaching band. The transition energy was found to be modulated periodically with the same frequencies of molecular vibration found in the Fourier amplitude spectrum of the difference absorbance real-time traces. This was interpreted to be due to the difference in the effective transition energy associated with the wavepacket motion induced by the equilibrium positions of potential curves between the ground state and the excited state. Using the values, Huang-Rhys factors for several vibrational modes involved in the spectral modulation at the room-temperature have been determined.