The plasmonic properties of an asymmetric dimer, comprising of two silver nanospheres with different radii, are studied by the finite difference time domain method. The extinction efficiencies of the plasmonic dimer are numerically calculated in the visible and near-infrared regime, i.e., from 950THz to 150THz. Two distinguishable Fano resonances are observed when the separation between the nanospheres is narrowed within a certain value, e.g., less than 10nm. The extinction spectrum that presents two Fano resonances, associated with two electromagnetic modes, is well fitted using a model consisting of two Fano lineshape functions. The resonance frequencies, the spectral widths, and the characteristic q values are obtained via the best fit parameters, and their trends are revealed with varying the radii of the nanospheres. The fitting scheme proposed in this work may be useful in the study of other plasmonic nanostructures with multiple Fano resonances.