We found that by fluorination of double-walled carbon nanotubes (DWNTs), it is possible to suppress only the Raman radial breathing mode and absorption peaks from the outer (large diameter) tubes of DWNTs. In contrast, Raman signals from the inner shells showed no difference from the pristine DWNTs. The stability of the inner shells of fluorinated DWNTs was also confirmed from the photoluminescence (PL) map and the optical absorption spectra, which only showed the signals from the inner shells of DWNTs, with no distinct change in the optical properties of the inner tubes after fluorination. Our results indicate that once fluorinated, there exists only a weak, if not none, interaction between the inner tube and the outer fluorinated tube, proving that fluorination can be used to suppress the optical properties of carbon nanotubes without interfering the properties of inner tubes. The present finding can be important in electronic and sensor applications, keeping the inner tube from having unwanted contact with other substances that may distract from the inner tube's own characteristics.