The 4f7 6s(9S)np 8PJ (J=5/2, 7/2, 9/2) Rydberg series converging to the first ionization limit 4f7 6s 9S4 of the Eu atom using the three-step laser excitation and electric-field-ionization (EFI) method are studied. First, the Eu atom is excited from the 4f7 6s2 8So7/2 ground state to the 4f76s7s 8So7/2 state through the 4f7 6s6p 10P9/2 state by the first two dye lasers. Next, it is populated to many higher-n members of the 4f7 6s(9S)np 8PJ Rydberg series by the third dye laser whose wavelength is scanned within a certain range. Finally, the atom in these higher-n states is ionized by the external pulsed electric field. With the field strength up to 2 kV/cm, we can detect the atom in 4f76s(9S)np 8PJ states with n>40. With the given laser line width, the level energies of Rydberg states with n as high as 72 can be determined. We not only confirm the previous data on the 4f76s(9S) np 8PJ Rydberg series, but also extend the n-value assignment significantly by detecting more states.