Eucalyptus plantations have widely expanded in the past two decades, which has triggered much debate with respect to their ecological and environmental impacts. One argument has focused on the organic carbon stocks of soil under Eucalyptus plantations. Although many studies have been devoted to this topic, the relationships between soil organic carbon density under a Eucalyptus plantation and terrain attributes are still unclear. In addition, little attention has been paid to secondary terrain attributes, as well as comparison of linear and non-linear relationships. This study was conducted in the Gaofeng Forest, a hilly area under Eucalyptus plantations with altitudes ranging from 125 m above sea level to 300 m in Nanning, China, and the linear and non-linear relationships between soil organic carbon density and terrain attributes (including both primary and secondary attributes) were investigated. A 10 m digital elevation model was constructed based on 1 ∶ 10000 digital topographic data of this area, and several commonly used terrain attributes, i.e., elevation, slope, aspect, plan curvature, profile curvature, and topographic wetness index, were extracted from the model. Then, the conditioned Latin hypercube sampling method was used to select representative samples based on these extracted terrain attributes. This method is a form of stratified sampling with the advantage of generating a set of samples that can precisely reflect the shape of a sampled distribution. Fifty sampling sites were selected using this method, of which only 41 were ultimately visited since the remaining 9 were not accessible. At each visited site, a soil profile was dug to the rocks or to a depth of 1.4 m. Soil samples were collected for each diagnostic layer of the profiles, which were then measured for soil organic carbon content using the potassium dichromate-oxidation method. Finally, correlation analysis, multiple linear regression, stepwise multiple linear regression, and regression tree modeling were explored to analyze relationships between the extracted terrain attributes and soil organic carbon density. In order to compare linear and non-linear relationships, pseudo-R² values, reflecting the spatial variability of soil organic carbon density explained by the models, were computed. The results showed that the 41 sampling sites represented the topographic conditions of this study area very well, as distributions of their terrain attributes were very similar to those of the whole study area. The soil organic carbon density within soil layer A, the 0-50 cm soil layer, and complete soil profile were 2.8 kg/hm², 7.7 kg/hm², and 10.9 kg/hm², respectively. However, only slope was correlated with the soil organic carbon density of soil layer A and the complete profile at a 0.05 level of significance. In general, primary terrain factors (i.e., elevation, slope, and aspect) were much more strongly correlated with soil organic carbon density than secondary factors (i.e., plan curvature, profile curvature, and topographic wetness index). This might be because the primary terrain attributes directly reflect redistribution of material and energy in the soil, whereas the secondary attributes can only reflect the overall environmental characteristics of soil. As soil depth increased, much more of the variability in soil organic carbon density was explained by the linear regression and non-linear tree models built from the terrain attributes. Comparatively, the non-linear tree models explained most of the variability of soil organic carbon density, followed by multiple linear regression models and stepwise regression models. Thus, it was concluded that non-linear relationships between soil organic carbon density under Eucalyptus plantations and terrain attributes are stronger than their corresponding linear relationships.