The invention relates to an illumination device (1) comprising an optical waveguide (2) and a number of (connections for) light sources (3)—especially LEDs—positioned along the waveguide (3). This waveguide has a central axis (4) at a distance r to the surface of the waveguide, said surface comprising a light entrance surface (6) on which the (connections for) light sources are positioned and a curved light exit surface (5), wherein, viewed along the circumference of the curved surface (5), the distance r to a first intersection (8) between the flat surface (6) and the curved surface (5), changes to a second distance of different value at the second intersection (9) between said surfaces. The invention also relates to a luminaire comprising such an illumination device (1). Due to the special design of the waveguide (2), the amount of reflections of light in the light sources is largely reduced and desired shaping of the exiting beam can be realized. The device can be further improved by the use of special features, like specially designed curved surfaces (5), reflective structures (13), channels (15) and torus-shaped waveguides.