Fine root traits and their relationships reflect the ecological trade-off strategies of plants in resource investment and are important for understanding the life strategies and growth of plants in response to changes in the environment. We used 16-year-old Chinese fir (Cunninghamia lanceolata Lamb. Hook.) plantations with different slope positions as the research object to explore the morphological, anatomical, and chemical properties of fine roots and their relationships. With increasing root order levels, the morphological, anatomical, and chemical traits of the fine roots of Chinese fir at different slope positions showed similar change trends; however, at the same order level, the differences were large. Under the upper slope site conditions, the average diameter of the second- and third-order roots and the thickness of the third-order root cortex were the highest. However, specific surface area, vascular bundle diameter, and the ratio of third-order roots were higher under the middle-slope site conditions. Under the lower slope site conditions, the specific surface area and specific root length of first-order roots and the root ratio of second-order roots were the highest. The biomasses of the first- and third-order roots on the middle and lower slopes were higher than those on the upper slope. The contents of N and P in fine roots of grades 1–3 Chinese fir showed the order of lower slope > middle slope > upper slope; however, the changes in C/N and C/P ratios showed the opposite trend, indicating differences in the morphological, anatomical, and chemical properties as well as resource acquisition strategies of fine roots of grades 1–3 Chinese fir under different slope positions. There were negative correlations between fine root diameter, N and P contents, and specific root length, indicating an acquisition and conservative resource trade-off relationships between fine root morphological, anatomical, and chemical traits. There were also differences in the relationships between the morphological, anatomical, and chemical traits of Chinese fir fine roots at different slope positions, indicating that the relationships between these traits were affected by slope position change. Chinese fir varieties with root-foraging characteristics ranging from resource conservation to resource acquisition can be selected for planting to improve the productivity of C. lanceolata plantations.