We present the results of a uniform and systematic search for blue-shifted Fe K absorption lines in the X-ray spectra of five bright Broad-Line Radio Galaxies (BLRGs) observed with Suzaku. We detect, for the first time at X-rays in radio-loud AGN, several absorption lines at energies greater than 7 keV in three out of five sources, namely 3C 111, 3C 120 and 3C 390.3. The lines are detected with high significance according to both the F-test and extensive Monte Carlo simulations. Their likely interpretation as blue-shifted Fe XXV and Fe XXVI K-shell resonance lines implies an origin from highly ionized gas outflowing with mildly relativistic velocities, in the range 0.04-0.15c. A fit with specific photo-ionization models gives ionization parameters in the range log_xi~4-5.6 and column densities of N_H~10^22-10^23 cm^-2. These characteristics are very similar to those of the Ultra-Fast Outflows (UFOs) previously observed in radio-quiet AGN. Their estimated location within ~0.01-0.3pc from the central super-massive black hole suggests a likely origin related with accretion disk winds/outflows. Depending on the absorber covering fraction, the mass outflow rate of these UFOs can be comparable to the accretion rate and their kinetic power can correspond to a significant fraction of the bolometric luminosity and is comparable to their typical jet power. Therefore, these UFOs can play a significant role in the expected feedback from the AGN on the surrounding environment and can give us further clues on the relation between the accretion disk and the formation of winds/jets in both radio-quiet and radio-loud AGN.