An accurate understanding of ion-beam transport in plasmas is crucial for applications in inertial fusion energy and high-energy-density physics. We present an experimental measurement on the energy spectrum of a proton beam at 270 keV propagating through a gas-discharge hydrogen plasma. We observe the energies of the beam protons changing as a function of the plasma density and spectrum broadening due to a collective beam-plasma interaction. Supported by linear theory and three-dimensional particle-in-cell simulations, we attribute this energy modulation to a two-stream instability excitation and further saturation by beam ion trapping in the wave. The widths of the energy spectrum from both experiment and simulation agree with the theory.