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Chromatic dispersion of dual-concentric-core photonic crystal fibers (PCFs), which have an inner low-index core and an outer high-index core, is investigated based on a full vector finite-element method. Large negative dispersion can be obtained by introducing avoided crossing between modes of the two asymmetric cores. While increasing the negative dispersion, larger effective mode area is also possible by choosing a higher order mode in the outer core to couple with the fundamental inner core mode. During the analysis, a dual-core PCF with a dispersion peak value of -36 000 ps/(nmldrkm) and effective mode area of 34.8 mum2 is presented.