In order to handle extremely-high stored energy in future proton-proton colliders, an extremely high-efficiency collimation system is required for safe operation. At LHC, the major limiting locations in terms of particle losses on superconducting (SC) magnets are the dispersion suppressors (DS) downstream of the transverse collimation insertion. These losses are due to the protons experiencing single diffractive interactions in the primary collimators. How to solve this problem is very important for future proton-proton colliders, such as the FCC-hh and SPPC. In this article, a novel method is proposed, which arranges both the transverse and momentum collimation in the same long straight section. In this way, the momentum collimation system can clean those particles related to the single diffractive effect. The effectiveness of the method has been confirmed by multi-particle simulations. In addition, SC quadrupoles with special designs such as enlarged aperture and good shielding are adopted to enhance the phase advance in the transverse collimation section, so that tertiary collimators can be arranged to clean off the tertiary halo which emerges from the secondary collimators and improve the collimation efficiency. With one more collimation stage in the transverse collimation, the beam losses in both the momentum collimation section and the experimental regions can be largely reduced. Multi-particle simulation results with the MERLIN code confirm the effectiveness of the collimation method. At last, we provide a protection scheme of the SC magnets in the collimation section. The FLUKA simulations show that by adding some special protective collimators in front of the magnets, the maximum power deposition in the SC coils is reduced dramatically, which is proven to be valid for protecting the SC magnets from quenching.