We investigate the properties of interstellar dust in the Galactic center region toward the Arches and Quintuplet clusters. With the Fourier Transform Spectrometer of the AKARI/Far-Infrared Surveyor, we performed the far-infrared (60 - 140 cm^-1) spectral mapping of an area of about 10 x 10 which includes the two clusters to obtain a low-resolution (R = 1.2 cm^-1) spectrum at every spatial bin of 30 x 30. We derive the spatial variations of dust continuum emission at different wavenumbers, which are compared with those of the [O III] 88 micron (113 cm^-1) emission and the OH 119 micron (84 cm^-1) absorption. The spectral fitting shows that two dust modified blackbody components with temperatures of ~20 K and ~50 K can reproduce most of the continuum spectra. For some spectra, however, we find that there exists a significant excess on top of a modified blackbody continuum around 80 - 90 cm^-1 (110 - 130 microns). The warmer dust component is spatially correlated well with the [O III] emission and hence likely to be associated with the highly-ionized gas locally heated by intense radiation from the two clusters. The excess emission probably represents a dust feature, which is found to be spatially correlated with the OH absorption and a CO cloud. We find that a dust model including micron-sized graphite grains can reproduce the observed spectrum with the dust feature fairly well.