Muon scattering tomography (MST) is a non-destructive technique to image various materials by utilizing cosmic ray muons as probes. A typical MST system with a two-fold track detectors is particularly effective in detecting high-Z materials (e.g. nuclear materials), but difficult to recognize low-Z materials (e.g. explosive materials). In this work, we present a concept of MST system to discriminate both low-Z and high-Z materials by extra measuring momentum of low-energy muons with a Cherenkov detector. A toy Monte Carlo simulation to describe detector responses and multiple scatterings of a muon tracking through materials is developed for statistical tests. Based on momentum-dependent track reconstruction and image reconstruction algorithm, we evaluate separation powers of different materials in the system. The results show that momentum measurement of low-energy muons and accurate track reconstruction can improve separation power of low-Z materials significantly. This may enable the MST system to detect both low-Z and high-Z materials with cosmic ray muons in the whole energy range.