This paper presents a novel dispersions equalization technique for multilayer core four-mode fiber using LP mode-matrix method. Each of the core ring radius of the alternating center-high (CH) and center-low (CL) index profile was optimized to a specific thickness value. The core ring radius varied in each case to determine the optimized thickness (OPT) for thn e dispersions equalization. The OPT of the center high index core fiber (CH) denoted by R1, R2, and R3 were found to be 4.25 μm, 2.6 μm, and 2.3 μm, respectively. Similarly, an OPT of the center low index core fiber (CL) which was denoted by X1, X2, X3, and X4 was found to be 2.0 μm, 3.0 μm, 4.20 μm and 1.60 μm, respectively. At 1.55 μm wavelength, these values were used to model the two fibers to achieve an equalized modal dispersion. It is the first time, to our knowledge, a core-ring radius of a CH, and CL index profile varied to a certain OPT value to achieve dispersion equalization. Fabrication challenges were also discussed in this paper.