A liquid crystal display apparatus and liquid crystal projection display apparatus, which employ a hologram color filter, and which are designed so that the illuminating light utilization efficiency is improved to a considerable extent, and that a color image can be faithfully displayed with excellent color reproducibility without uneven color or other similar problem. A color liquid crystal display apparatus (11) has a hologram (5), which diffractively disperses incident light so as to emanate light rays in different wavelength regions at a predetermined spatial period, as a color filter, and a liquid crystal display device (6). The display apparatus (11) is illuminated by white parallel back light (3) from an illuminator (14). A displayed image which is modulated in the color liquid crystal display apparatus (11) is passed through a field lens, which is disposed in the vicinity of the display apparatus (11), and formed as an enlarged image on a screen (19) for display through a projection lens (18). A short-wavelength cut-off filter whose transmittance for a wavelength not longer than 430 nm is not higher than 5% is disposed at a position in an optical path extending from a lamp (15) to the screen (19), thereby preventing crosstalk of colors which might otherwise occur when light which should be incident on a pixel assigned to display blue undesirably enters a pixel which is adjacent to the pixel for blue, and thus making it possible to display a faithful color image.