Cosmic ray muons have been considered as a non-conventional radiation probe in various applications. To utilize cosmic ray muons in engineering applications, two important quantities, trajectory and momentum, must be known. The muon trajectories are easily reconstructed using two-fold detector arrays with a high spatial resolution. However, precise measurement of muon momentum is difficult to be achieved without deploying large and expensive spectrometers such as solenoid magnets. Here, we propose a new method to estimate muon momentum using multi-layer pressurized gas Cherenkov radiators. This is accurate, portable, compact (< 1m3), and easily coupled with existing muon detectors without the need of bulky magnetic or time-of-flight spectrometers. The results show that not only our new muon spectrometer can measure muon momentum with a resolution of ±0.5 GeV/c in a momentum range of 0.1 to 10.0 GeV/c, but also we can reconstruct cosmic muon spectrum with high accuracy (~90%).