A velocity-map-imaging (VMI) method is employed to investigate systematically the dynamical process of ejected electrons from autoionizing states of the Eu atom for the first time as far as we know. An atom is excited stepwise from the 4f76s6s8 S7/2 ground state to the 4f76s8s8 P7/2 Rydberg state via the 4f76s6p6 P5/2 intermediate state, then further excited to the 4f76p1/2(J=3)8s and 4f76p1/2(J=4)8s autoionizing states using the three-step isolated-core excitation method. According to the excitation pathways and selection rules, the value of total angular momentum of the autoionizing state can be calculated. The energy conservation and angular momentum parity conservation would enable us to determine the final states during the autoionizing process. The ejected electron, which decays from the autoionizing process, can be focused and imaged by the electron lens and the kinetic energy of it is resolved by the position sensitive detector. By combining velocity-map-imaging method with the mathematical transformation, the ejected electron energy distribution can be obtained, also the branching ratio is confirmed. Simultaneously, by tuning the wavelength of the third laser, the characteristic of the branching ratio following the variation of the photon energy, and the possibility of the population inversion have been discussed.