An illumination system for illuminating a display device (3) comprises a light-emitting panel (1) having a light-emission window (2) and at least one edge surface (4) for coupling light into the light-emitting panel (1). The illumination system further comprises a light mixing chamber (5) provided with a light source (6). The light mixing chamber (5) is associated with the edge surface (4). According to the invention, the light source (6) comprises a plurality of clusters of light-emitting diodes (LEDs) having different light-emission wavelengths, the clusters being arranged at a pitch P with respect to each other. The ratio of the height H of the light mixing chamber (5) to the pitch P of the clusters meets the relation 0.1≦H/P≦10, preferably 0.2≦H/P≦2. Preferably, each cluster comprises one blue, one green and one red LED, or one blue, two green and one red LEDs. Preferably, each LED has a luminous flux of at least 5 lumen. The illumination system according to the invention has a very uniform light distribution, so that the display device is uniformly illuminated.