In an XMM-Newton observation of the east lobe of nearby radio galaxy Fonrax A, we have significantly detected the diffuse X-ray emission, which was originally discovered by ASCA and ROSAT. The X-ray spectrum of the diffuse emission is described by a single power-law model, modified with the Galactic absorption toward the object. The best-fit X-ray photon index, 1.62 -0.15,0.25 agrees well with the synchrotron radio index, 1.68 ±0.05, between 29.9 MHz and 5 GHz. Therefore, the inverse Compton interpretation for the diffuse X-ray emission is justified. A comparison between the radio and X-ray flux densities gives a moderate electron-energy dominance over in the east lobe of Fornax A, in spite of the dormancy of its nucleus. We also reexamined the ASCA result on the west lobe, to find that both lobes share the similar physical condition.