Dense high-energy monoenergetic proton beams are vital for wide applications, thus modern laser-plasma-based ion acceleration methods are aiming to obtain high-energy proton beams with energy spread as low as possible. In this work, we put forward a quantum radiative compression method to post-compress a highly accelerated proton beam and convert it to a dense quasi-monoenergetic one. We find that when the relativistic plasma produced by radiation pressure acceleration collides head-on with an ultraintense laser beam, large-amplitude plasma oscillations are excited due to quantum radiation-reaction and the ponderomotive force, which induce compression of the phase space of protons located in its acceleration phase with negative gradient. Our three-dimensional spin-resolved QED particle-in-cell simulations show that hollow-structure proton beams with a peak energy $sim$ GeV, relative energy spread of few percents and number $N_psim10^{10}$ (or $N_psim 10^9$ with a $1%$ energy spread) can be produced in near future laser facilities, which may fulfill the requirements of important applications, such as, for radiography of ultra-thick dense materials, or as injectors of hadron colliders.
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