Landscape evolution models (LEMs) are essential tools for analyzing tectonic-climate interactions and reproducing landform-shaping processes. In this study we used a LEM to simulate the evolution of the mountains from the central Hexi Corridor in the northeastern Tibetan Plateau, where the climate is arid and the surface processes are relatively uniform. However, there are pronounced differences in the topography between the mountains around the central Hexi Corridor. The East Jintanan Shan, West Jintanan Shan and Heli Shan are located in the northern part of the corridor; and the Yumu Shan in the southern part. Firstly, several representative areas were selected from these mountains to analyze the topographic characteristics, including the uniform valley spacing, local relief, and the outlet number. Secondly, a LEM for these areas was constructed using the Landlab platform, and the landscape evolution was simulated. With uniform valley spacing and other topographic characteristics as the criteria, we compared the realistic and simulated terrain for different model ages. Finally, based on the similarity of the simulated and realistic terrain, we estimated the timing of the initial uplift and the uplift rate of the four mountain ranges. The results are consistent with previous geological and geomorphological records from these youthful stage mountains that have not yet reached a steady state. Our findings demonstrate that LEMs combined with topographic characteristics are a reliable means of constraining the timing of the initial uplift and the uplift rate of the youthful stage mountain. Our approach can potentially be applied to other youthful stage mountains and it may become a valuable tool in tectonic geomorphology research.