We report an experimental measurements of K+-meson production in p-p collisions at 2.85 and 2.40 BeV. The momentum spectra of the K+ mesons are given at the three laboratory angles of 0°, 17°, and 32°. The K+ mesons were identified by momentum and velocity using differential Čerenkov counters with a combined rejection of the order of 10-6. It is shown that the production spectra can be accounted for by a one-meson-exchange mechanism with the introduction of appropriate cutoffs. At the high-energy limit of the 0° spectrum, a clear peak is observed, which is attributed to the low-energy Λ-p interaction in the KΛp final state. No other enhancements or pronounced effects due to resonances either in the Yp or KY system are observed.