A new ion acceleration method, namely, phase-stable acceleration, using circularly-polarized laser pulses is proposed. When the initial target density n(0) and thickness D satisfy a(L) approximately (n(0)/n(c))D/lambda(L) and D>l(s) with a(L), lambda(L), l(s), and n(c) the normalized laser amplitude, the laser wavelength in vacuum, the plasma skin depth, and the critical density of the incident laser pulse, respectively, a quasiequilibrium for the electrons is established by the light pressure and the space charge electrostatic field at the interacting front of the laser pulse. The ions within the skin depth of the laser pulse are synchronously accelerated and bunched by the electrostatic field, and thereby a high-intensity monoenergetic proton beam can be generated. The proton dynamics is investigated analytically and the results are verified by one- and two-dimensional particle-in-cell simulations.