Based on the cross-spectral density (CSD) function, the coherence-orbital angular momentum (COAM) matrix of twisted Gaussian Schell-model (TGSM) beam is proposed, and the COAM matrix is used to describe the correlation between OAM modes in TGSM optical field. The COAM matrix characteristics of TGSM beam are analyzed by numerical simulation. The results show that the COAM matrix characteristics of TGSM beam depend on the initial parameters of the beam. In addition, a method of generating TGSM beam by superposition of COAM matrix element modes is described, and the influence of different initial parameters on the superposition characteristics is studied. The results reveal the internal relationship between the coherent structure of the optical field, the twist phase and the OAM modes. Our work helps to explore new expressions of partially coherent beams and promote the practical application of optimizing partially coherent beams.