Comet 21P/Giacobini-Zinner (hereafter, comet 21P/G-Z) is a Jupiter-family comet and a parent comet of the October Draconids meteor shower. If meteoroids originating from a Jupiter-family comet contain complex organic molecules, such as amino acids, they are essential pieces of the puzzle regarding the origin of life on Earth. We observed comet 21P/G-Z in the mid-infrared wavelength region using the Cooled Mid-infrared Camera and Spectrometer (COMICS) on the 8.2 m Subaru Telescope on UT 2005 July 5. Here, we report the unidentified infrared (UIR) emission features of comet 21P/G-Z, which are likely due to complex organic molecules (both aliphatic and aromatic hydrocarbons), and the thermal emission from amorphous/crystalline silicates and amorphous carbon grains in its mid-infrared low-resolution spectrum. The UIR features at ~8.2 µm, ~8.5 µm, and ~11.2 µm found in the spectrum of comet 21P/G-Z could be attributed to polycyclic aromatic hydrocarbons (or hydrogenated amorphous carbons) contaminated by N-or O-atoms, although part of the feature at ~11.2 µm comes from crystalline olivine. The other feature at ~9.2 µm might originate from aliphatic hydrocarbons. Comet 21P/G-Z is enriched in complex organic molecules. Considering that the derived mass fraction of crystalline silicates in comet 21P/G-Z is typical of comets, we propose that the comet originated from a circumplanetary disk of giant planets (similar to Jupiter and Saturn) where was warmer than the typical comet-forming region (5-30 au from the Sun) and was suitable for the formation of complex organic molecules. Comets from circumplanetary disks might be enriched in complex organic molecules, such as comet 21P/G-Z, and may have provided pre-biotic molecules to ancient Earth by direct impact or meteor showers.