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Purpose – Since the construction of China-ASEAN Free Trade Area (CAFTA) launched in 2002, the bilateral trade increased rapidly. The purpose of this paper is to test the competition and cooperation in trade relationships between China and the main trading partners (Singapore, Malaysia and Thailand (SMT)) from ASEAN in international trade under CAFTA. Design/methodology/approach – Grey Lotka-Volterra competition models are established for testing the trade relationships between China and SMT, respectively, based on the data of import and export from 2003 to 2014. To improve modeling accuracy, the interpolated coefficients for dynamic background value are introduced into the grey Lotka-Volterra model. The optimal parameters are solved through minimizing the mean absolute percentage error and the constraint of parameter relationships. Besides, eigenvalues of the Jacobian matrix are adopted to carry out the stability of equilibrium points of the trade relationships. Findings – As the beneficiary party, China has mutual benefit and win-win trade relationship with Singapore, while it has predator-prey trade relationships with Malaysia and Thailand. The future exports from SMT to China will stabilize at 462.31, 598.13 and 447.03 billion dollars, respectively. The future exports from China to SMT will stabilize at 637.16, 943.71 and 827.52 billion dollars, respectively. Practical implications – This study can be regarded as an important reference for China and its trading partners from ASEAN. The modeling results can help the decision makers to formulate appropriate international trade strategies to gain and maintain competitive advantages. Originality/value – A new approach to testing the trade relationships is proposed based on grey Lotka-Volterra competition model. The study also proposed a dynamic optimization method for the background value of grey Lotka-Volterra model. [ABSTRACT FROM AUTHOR]