A new mechanism is suggested to explain the formation of proton beam velocity distributions in high-speed streams of the solar wind. The proton beam is a well-known kinetic phenomenon, which was already found in the early days of solar wind in situ measurements <Feldman et al., 1973; Marsch et al., 1982a; Rosenbauer et al., 1981>. Observationally, proton beams move faster than the core part of the proton distribution by more than the Alfv¿n speed. The beam has a higher temperature than the core, but the thermal anisotropy is usually smaller. Until today none of the major properties of the observed beams have been adequately explained. The basic difficulty faced by previous investigations is that in a proton-electron plasma, hardly any cyclotron waves are found to be in resonance with the beam protons. However, when considering a proton-alpha-electron plasma, we find a second dispersion branch of outward propagating RHP and LHP waves. This branch is mainly determined by the alpha particles drifting at the Alfv¿n speed. The associated waves can resonate with the beam protons, and the resulting cyclotron-resonance-induced diffusion produces a beam velocity distribution. The time-dependent two-dimensional diffusion equation, as determined from the quasi-linear theory of ion cyclotron-wave resonance, is solved numerically. A proton beam distribution is shown to form, by diffusion in the wave field, out of an initial shuttle-like bi-Maxwellian velocity distribution function. The drift velocity of the model beam is about the Alfv¿n speed. The perpendicular thermal speed is about 44 km/s, and the thermal anisotropy of the beam is much less than the core anisotropy. Limitations of the present model and work to be done in the future are also discussed.