The present invention is directed to an apparatus and method for displaying 3D images. The apparatus comprises: a) a screen with angular dependent diffusion characteristics for direction selectively forwarding light; b) a screen illuminating system, the screen illuminating system comprising multiple modules for generating multiple light beams incident on points of the screen, the modules being arranged so that each point of the screen is illuminated by multiple modules, and the incident light beams generated by one module are projected into multiple different directions from the module towards multiple different points of the screen, and further the different incident light beams generated by one module are forwarded towards different emitting directions from the screen, means for coding each incident light beam with the image information of a single image point in the module, where the 3D image perceived by an observer being generated by multiple modules; c) a control system to control the modules; and d) means for imparting an exit divergence to the exiting light beams being transmitted through or reflected from the screen, the measure of the exit divergence substantially corresponding to the angle between neighbouring emitting directions associated with the optically neighbouring modules, go as to provide a substantially continuous motion parallax in the 3D image perceived by an observer. The apparatus according to the invention comprises imaging means for generating the incident light beams with a convergent section converging substantially towards a point of the screen, where a convergence of the incident light beams is substantially equal to the exit divergence of the light beams exiting the screen. The modules can be video projectors, LED projectors, the optical engines of these, or the like, arranged periodically shifted, preferably in the horizontal direction and the diffuser screen is realised as a holographic screen, arrays of diffractive or refractive elements, retroreflective surfaces, or any combination thereof, for imparting a larger divergence to the exit light beams along at least one, preferably in the vertical direction, while in the other direction the angle of divergence provided by the screen is smaller than the angle between the neighbouring emitting directions associated with the optically neighbouring modules. The invention is also directed to a method implemented by the apparatus according to the invention.