Water and oil detection is important for machine vision applications such as visual inspection and robot motion planning. It is known that water absorbs near infrared light and oil absorbs near ultraviolet and blue light. Therefore, observing at the absorbed wavelengths, the apparent spectral reflectances of surfaces with water/oil are smaller than that without water/oil. We could detect water/oil based on the above absorption features by using a hyperspectral image, if the original spectral reflectances of surfaces are known. However, in general, the spectral reflectances of surfaces are unknown and spatially varying. In this paper, we propose a novel per-pixel water and oil detection method based on the Lambert-Beer's law and a low-dimensional linear model for spectral reflectance. We show that our method enables us to pixelwisely detect water and oil on surfaces with unknown and spatially-varying reflectance at high accuracy by using a hyperspectral image. The effectiveness of our proposed method is confirmed through a number of experiments using real hyperspectral images.