The LEAP (Low-Energy Antiproton) experiment is a search for cosmic-ray antiprotons in the 120 MeV to 1.2 GeV kinetic energy range. The motivation for this project was the result announced by Buffington et al. (1981) that indicated an anomalously high antiproton flux below 300 MeV; this result has compelled theorists to propose sources of primary antiprotons above the small secondary antiproton flux produced by high energy cosmic-ray collisions with nuclei in the interstellar medium. LEAP consisted of the NMSU magnet spectrometer, a time-of-flight system designed at Goddard Space Flight Center, two scintillation detectors, and a Cherenkov counter designed and built at the University of Arizona. Analysis of flight data performed by the high-energy astrophysics group at Goddard Space Flight Center revealed no antiproton candidates found in the 120 MeV to 360 MeV range; 3 possible antiproton candidate events were found in the 500 MeV to 1.2 GeV range in an analysis done here at the University of Arizona. However, since it will be necessary to sharpen the calibration on all of the LEAP systems in order to positively identify these events as antiprotons, only an upper limit has been determined at present. Thus, combining the analyses performed at the University of Arizona and Goddard Space Flight Center, 90% confidence upper limits of 3.5 x 10⁻⁵ in the 120 MeV to 360 MeV range and 2.3 x 10⁻⁴ in the 500 MeV to 1.2 GeV range for the antiproton/proton ratio is indicated by the LEAP results. LEAP disagrees sharply with the results of the Buffington group, indicating a low antiproton flux at these energies. Thus, a purely secondary antiproton flux may be adequate at low energies.