For a number of applications, it is essential to design fibers that exhibit nearly zero ultra-flattened chromatic dispersion. Moreover, the nearly zero ultra-flattened chromatic dispersion fiber should ensure the single mode operation to avoid the multimode dispersion as it is responsible for signal degradation. In order to control the nearly zero ultra-flattened chromatic dispersion and single-mode regime, the present paper describes a new controlling technique of a dual concentric core fiber (DCCF). The finite element method (FEM) is used to investigate the properties. By introducing a varying index profile (alpha) in the core region of the DCCF, we can successfully design a single-mode operation fiber with nearly zero ultra-flattened chromatic dispersion in linear or nonlinear application. Other important guiding characteristics such effective mode area (Aeff), effective nonlinear refractive index (n2) are also discussed. The proposed DCCFs can be applicable in digital optical communication (dense wavelength division multiplexing (WDM) systems, for long-haul telecommunications networks and super continuum generation (SCG)).