Competition in forests plays a significant role in the process of tree growth, and the competition indices were typically used to quantify the intensity of competition among individual trees. However, due to the rich composition of tree species and the patchy distribution in natural mixed forests, there were still few studies on tree competition in natural mixed forests. In this study, we constructed a competition index based on the overlapped area of tree crowns and interspecies interactions, which allowed us to investigate the intensity of competition in natural forests and among major tree species. Specifically, we focused on the Quercus aliena natural forest in Xiaolongshan Forest District of Gansu Province and used data of DBH (breast height diameter), tree height, crown size, and distance from two surveys to validate the newly developed CIM (Competition Index based on Overlapping area and Mixing) index. To evaluate the effectiveness of our index, we utilized the CIM and conventional competition indices, such as CIO (Competitive Influence-Zone Overlap) and CI (Competition Index), and employed the Spearman coefficient to analyze their correlation with growth accumulation. We found that our method of determining competing trees using crown projection overlaps and tree height was an effective tool that could help prevent excessive selection or omission of competing trees. The results indicated that CIM1, CIM2, and CIM3 could effectively capture changes in competition pressure across natural forests and demonstrated that as competition pressure increased, tree growth accumulation decreased. In addition, by introducing the tree species mixing factor into our competition indices, we improved the correlation between growth accumulation and competition indices and provided a more objective representation of competition status in the natural forest. Specifically, our study found that the correlation between competition indices and growth accumulation was the highest for CIM2, followed by CIM3, CIM1, CIO, CI, CIO2, and CIO1. The competition index CIM2 provided more comprehensive information regarding competition within the mixed forests. Our investigation into the competitive pressures of Quercus aliena revealed that the intensity of competition increased with the number of intraspecies competing trees in close proximity. Given the complex and diverse species composition and patchy distribution of trees in mixed forests, it is critical to introduce sufficient factors into competition indices to obtain a reasonably accurate representation of the competitive relationship between trees. Overall, our study provided an effective method for expressing the competitive relationship between trees in natural mixed forests and demonstrated the importance of considering multiple factors when measuring competition intensity.