As crude oil demand grows, the international crude oil trade grows as well, thus import trade competition between crude oil importers intensifies. It further leads to the increasing import pressure faced by importers. We defined and calculated the import competition pressure. Taking crude oil importers as nodes, the import competition relationships between importers as edges, the direction of import competition pressure as the edges’ direction, and the crude oil importing competitive pressures forced on importers are weights, the paper builds a crude oil import trade competition pressure network. Using a complex network theory analysis method, according to complex network characteristics, the paper analyzes crude oil import trade competition pressure network evolution law from 2000 to 2020. The results showed that: (1) The import competition intensity difference is larger, concentrated between Asian and European countries; (2) The most import competitive markets for crude oil are Russia and Saudi Arabia, and the crude oil dependence of China on Saudi Arabia is higher than USA; (3) The crude oil trade relationships are roughly divided into four categories, namely import-dependence, importer-oriented, close cooperation, and loose trade relationships; (4) China has gotten increasing competitive pressure from Germany and Netherlands in Russia in recent years, but decreasing in Angola and Saudi Arabia. Based on the above results, we recommend diversifying the supply, expanding the global circle of trusted trading partners and establishing a risk response mechanism. The above analysis can help countries identify competition pressure and provide suggestions for improving competitive advantages about crude oil.