The coherent backlight unit (C-BLU) using a diffractive optical element (DOE) for full-color flat-panel holographic display is proposed. The coherent backlight unit is composed of two diffractive optical elements (DOEs) that are imprinted on the same glass substrate. The illumination area of the backlight is 250 mm x 130 mm and the thickness is 2.2 mm, which is slim compared to other conventional coherent backlight units for holographic display systems. In experiments, the total efficiency is measured as 0.8% at red (638 nm), 3.9% at green (520nm), and 3.4% of blue (473 nm). As a result, we could get the 10 inch full color holographic display with 4k resolution.