A dual-concentric-core photonic crystal fiber (DCPCF) with low germanium doping is numerically investigated for dispersion compensation. The inner cladding is formed by a fluorine-doped concentric ring which is used to increase the index slope difference between two supermodes and eliminate the sensitivity of dispersion characteristic to air holes in the inner cladding of traditional structures. The proposed DCPCF can compensate for the dispersion and dispersion slope of a standard single-mode fiber (SMF) at 1550-nm wavelength. The $K$ value matches with that of SMF very well. Moreover, it can realize an effective compensated dispersion range of ±0.8 ps/nm/km from 1.458 to $1.626~\mu \text{m}$ wavelength which covers the $S+C+L$ bands. The geometric parameters on dispersion characteristic are investigated. The sensitivity of the fiber dispersion and the effective compensated dispersion to ±2% and ±5% variation in the optimum parameters is studied for practical fabrication.