A novel hexangular lattice dual-concentric-core photonic crystal fiber is proposed, which is composed of a central defect core, an outer ring core by introducing small air-holes on the forth ring and double cladding circle air-holes along the direction of fiber length. Based on full vector finite element method with anisotropic perfectly matched layers, its dispersion, nonlinear, leakage loss and mode field are numerically investigated. Numerical results indicate that the proposed fiber shows higher negative dispersion tunable effect and stronger confinement ability of guided mode, which the leakage loss is close to 10-2 dBm-1. The wavelength for high negative dispersion value can be adjusted by artificially choosing the parameters of proposed fiber, i.e. , d1 and f. Both its dispersion and dispersion slope are negative, the dispersion slope values are between-1-6 pskm-1nm-2 over C band, and its negative dispersion value is-3400 pskm-1nm-1, the nonlinear coefficient is only 3.6 km-1W-1, and the corresponding area of mode field is 43 m2 at wavelength of 1.55 m, if the parameter is selected as =1.2 m, f=0.917, d1=0.515 m. Obviously, it has a good dispersion compensation, therefore it has admirable applications in the field of high-speed large-capacity high-power pulses long-distance communication system.