Abstract Green Peas represent a population of compact, highly star-forming dwarf galaxies at redshifts z  ∼ 0.2–0.3 that have recently been found to show signatures of ultraviolet ionizing radiation leakage. They are being considered as analogs to high-redshift star-forming galaxies, possibly responsible for cosmic reionization. Despite intensive studies of Green Peas in the ultraviolet and optical domains, their X-ray properties have only so far been probed by nearby analogs. In this paper, we present the first measurements of Green Peas in the X-ray domain to constrain their spectral properties and fluxes at high energies. We analyzed XMM-Newton observations of three Green Pea sources. For two of them, we found an X-ray luminosity exceeding by a half-order of magnitude its predicted value, derived from the star formation rate and metallicity. Only an upper limit of the X-ray luminosity was derived for the third studied galaxy. Our results indicate that at least some Green Peas produce copious amounts of highly energetic photons, larger than detected in other star-forming galaxies. We discuss possible physical scenarios for the measured X-ray excess, including the presence of a hidden active galactic nucleus, a larger population of X-ray binaries, or ultra-luminous X-ray sources. Future spatially resolved X-ray images will discriminate between the models. Larger Green Pea samples will provide a possible link between the X-ray properties and the leaking ultraviolet radiation.