In this work, Chalcogenide coaxial fiber has been studied with step refractive indices in the inner and outer cores for dispersion compensation in the region of wavelength from 1.46 µm to 1.62 µm employing simple coupled mode analysis for the first time according to our knowledge. In designing the coaxial fiber structure, we have considered three values for a fixed value where and are respectively large and small relative refractive index differences. The effects of change in on the effective refractive indices, phase matching wavelengths (PMWs), and the dispersion coefficients with variation of wavelength of the coaxial fiber have been studied and reported in this paper. The maximum value of negative dispersion coefficients -1627 ps/nm-km, -1542 ps/nm-km and -1455 ps/nm-km are found at PMWs 1.511 µm, 1.550 µm, and 1.586 µm respectively. The choice of different is enabling the maximum negative dispersion peak and the PMW to be tuned inside the wavelength window of optical communication. The proposed coaxial fiber will exhibit much importance in the field of optics and photonics.