We propose a new nano-imaging technique for intrinsic absorption properties of materials under a platform of conventional aperture-less near-field scanning optical microscopy (NSOM). In aperture-less NSOM, when a silicon nanotip is utilized and illuminated by the visible light instead of a metallic tip, Raman scattering of silicon from the tip apex can be obtained. Since the wavelength of this Raman scattered light is shifted to 520cm-1 from the one of the excitation light, far-field background signal excited by the diffraction limited focus spot of the incident light, which is one of the major problems in aperture-less NSOM, can be avoided. When the silicon nano-tip is on the sample and illuminated, the Raman signal of silicon can be partially absorbed by the sample while passing through it, so that measuring the intensity of the Raman signal of silicon enables us to observe the absorption behavior of the sample at nano-scale. Because the absorbance of light is dependent on the absorption coefficient of the sample as well as its sample topography, it is needed to eliminate the effect of the sample topography from the absorption measurement to technically evaluate the absorption coefficient of the sample. For this purpose, we simultaneously employed two different incident lasers and utilized absorbance ratio between two wavelengths to monitor the absorption coefficient of the sample. As an example, we demonstrated that two types of carbon nanotubes, which have different absorption properties, could be clearly distinguished with nano-scale resolution by our technique.