Photoelectron spectroscopy has been performed to study the multiphoton double ionization of Ar in an intense extreme ultraviolet laser field (hν ∼ 21 eV, ∼ 5 TW/cm²), by using a free electron laser (FEL). Three distinct peaks identified in the observed photoelectron spectra clearly show that the double ionization proceeds sequentially via the formation of Ar(+): Ar+hν→Ar (+) + e⁻ and Ar²(+) + 2hν→Ar(+) + e⁻. Shot-by-shot recording of the photoelectron spectra allows simultaneous monitoring of FEL spectrum and the multiphoton process for each FEL pulse, revealing that the two-photon ionization from Ar(+) is significantly enhanced by intermediate resonances in Ar(+).