Cosmic-ray muon is a kind of charged particle with strong penetrating capability and sensitivity to high atomic number materials. In recent years, muongraphy emerged as a novel technique by using cosmic-ray muon to image unknown volume, and is widely applied to nuclear security, geosciences, archaeology and civil engineering. The effect of multiple Coulomb scattering between muons and materials with different atomic number is different, and the scattering angle is related to material Zand muon energy. If we can measure muon scattering angle and muon energy, we can identify the category of material interacted with muon. However, it is difficult to measure the energy of each muon in real time, most of the researches use the mean muon energy ~4 GeV to alternate each muon energy which causes image to blurred and material discrimination accuracy to decrease. This article introduces a method of using the discrete muon energy to fit the scattering angle distribution derived from continuous muon energy and estimate the weight of each discrete muon energy. Then measure the scattering angle of the material to be identified, histogram the scattering angle and couple it with the calibrated scattering angle distribution by discrete muon energy. The last step is to calculate the radiation length from the above equation. The radiation length is a characteristic quantity of the material, and used to identify materials in this method. We carry out the experiment on material’s discrimination based on the apparatus of cosmic-ray muon tomography made by China Institute of Atomic Energy. The system contains 6 layers, consisting of several drift tube detectors planted in two orthogonal coordinate for tracking muon trajectory. Five materials are selected to be distinguished in the experiment, they being C, Al, Fe, Pb, and W. The scattering angles formed by muons passing through these materials are measured respectively, and their radiation lengths are measured and identified in pairs. In order to evaluate material discrimination accuracy, we plot the ROC curve between each pair of materials. The result reveals that Al-Fe and Fe-Pb can be effectively identified at a 95% confidence level, under 1400 valid muon events. Considering that the difference in material density also influences discrimination accuracy, we simulate several other materials identified by Pb. It is concluded that this method can identify the materials with radiation length greater than 0.7 cm. Compared with the discrimination method of unknowing muon energy, this method improves the accuracy of Pb-W discrimination by 18.5%.