In both particle physics and cosmic ray muon applications, a high-resolution muon momentum measurement capability plays a significant role not only in providing valuable information on the properties of subatomic particles but also in improving the utilizability of muons. Currently, muon momentum is estimated by reconstructing the muon path using a strong magnetic field and muon trackers. Alternatively, time-of-flight or multiple Coulomb scattering techniques are less frequently applied, especially when there is a need to avoid using a magnetic field. However, the measurement resolution is much lower than that of magnetic spectrometers, approximately 20% in the muon momentum range of 0.5 to 4.5 GeV/c whereas it is nearly 10% or less when using magnets and trackers. Here, we propose a different paradigm to estimate muon momentum that utilizes multi-layer pressurized gas Cherenkov radiators. Using the fact that the gas refractive index varies with pressure and temperature, we can optimize the muon Cherenkov threshold momentum for which a muon signal will be detected. By analyzing the optical signals from Cherenkov radiation, we show that the actual muon momentum can be estimated with a minimum resolution of +-0.05 GeV/c for a large number of radiators over the range of 0.1 to 10.0 GeV/c. The results also show that our spectrometer correctly classifies the muon momentum (~87% classification rate) in the momentum range of 0.1 to 10.0 GeV/c. We anticipate our new spectrometer will to provide an alternative substitute for the bulky magnets without degrading measurement resolution. Furthermore, we expect it will significantly improve the quality of imaging or reduce the scanning time in cosmic muon applications by being incorporated with existing instruments.