The asymmetric dual-core fiber (ADCF) is proposed to obtain large group velocity dispersion (GVD) because of the coupling effects between the fundamental modes of the central core and high-order modes of the side core. The supermodes of the ADCF can provide anomalous- and normal-GVD profiles with large peak values at the maximum dispersion wavelengths. The maximum dispersion wavelengths can be shifted in the wavelength window of 1 550 nm by properly tuning the refractive indexes and diameters of the cores or spacing between the two cores. Furthermore, the numerical results show that the ADCF with the normal-GVD supermode 1 can be employed in the pulse broadening, where the broadening factor can reach more than 30 without pulse distortion from nonlinear effects.