We derive the extinction curve toward the Galactic center (GC) from 1 to 19 Delta *mm. We use hydrogen emission lines of the minispiral observed by ISO-SWS and SINFONI. The extinction-free flux reference is the 2 cm continuum emission observed by the Very Large Array. Toward the inner 14'' X 20'', we find an extinction of A 2.166 Delta *mm = 2.62 ? 0.11, with a power-law slope of Delta *a = --2.11 ? 0.06 shortward of 2.8 Delta *mm, consistent with the average near-infrared slope from the recent literature. At longer wavelengths, however, we find that the extinction is grayer than shortward of 2.8 Delta *mm. We find that it is not possible to fit the observed extinction curve with a dust model consisting of pure carbonaceous and silicate grains only, and the addition of composite particles, including ices, is needed to explain the observations. Combining a distance-dependent extinction with our distance-independent extinction, we derive the distance to the GC to be R 0 = 7.94 ? 0.65 kpc. Toward Sgr A* (r < 05), we obtain AH = 4.21 ? 0.10, AKs = 2.42 ? 0.10, and A L' = 1.09 ? 0.13.