Topographic correction can reduce the influences of topographic factors and improve the accuracy of forest tree species classification when using remote-sensing data to investigate forest resources. In this study, the Mount Taishan forest farm is the research area. Based on Landsat 8 OLI data and field survey subcompartment data, four topographic correction models (cosine model, C model, solar-canopy-sensor (SCS)+C model and empirical rotation model) were used on the Google Earth Engine (GEE) platform to carry out algorithmic data correction. Then, the tree species in the study area were classified by the random forest method. Combined with the tree species classification process, the topographic correction effects were analyzed, and the effects, advantages and disadvantages of each correction model were evaluated. The results showed that the SCS+C model and empirical rotation model were the best models in terms of visual effect, reducing the band standard deviation and adjusting the reflectance distribution. When we used the SCS+C model to correct the remote-sensing image, the total accuracy increased by 4% when using the full-coverage training areas to classify tree species and by nearly 13% when using the shadowless training area. In the illumination condition interval of 0.4–0.6, the inconsistency rate decreased significantly; however, the inconsistency rate increased with increasing illumination condition values. Topographic correction can enhance reflectance information in shaded areas and can significantly improve the image quality. Topographic correction can be used as a pretreatment method for forest species classification when the study area’s dominant tree species are in a low light intensity area.