In order to obtain a new elliptically twisted multi-Gaussian-Schell model beam, a Mercer model expansion method was adopted, the theoretical analysis and verification were carried out. It is proved that the twisted phase can be carried in the multi-Gaussian-Shell model correlation structure, and the intensity and coherence evolution of the beam propagating in gradient index fibers was studied. The results show that when elliptically twisted multi-Gaussian-Schell model beams are propagating in the graded index fibers, the distribution of intensity and coherence rotates periodically with the increase of transmission distance, and the deflection is π/2 degrees at the integer multiples of 0.5L (L is a cycle). The rotation angular velocity is nonlinear and related to the size of the twist factor. With the increase of multi-Gaussian modulus, the flat top region of the intensity distribution at the focal plane increases, and the coherence distribution contour becomes smaller. The research results have potential applications in optical fiber communication, focused imaging, optical capture and so on.