The development of light-emitting diodes (LEDs) of different emission spectra is revolutionizing lighting technology and opening up completely new applications and research areas. The spectral irradiance of the sun reaching the Earth's surface is very complex due to radiative transfer processes within the atmosphere and ranges from the shortwave ultraviolet (UV) to longwave infrared (IR) radiation. The simulation of this spectral irradiance by artificial light sources is technically very demanding. It could be realized sufficiently so far by a combination of different light sources, mostly light bulbs, metal halide lamps and fluorescent tubes, in combination of different filters. In the present work, we are presenting a new LED Sun Simulator system, which allows simulating spectral irradiance close to natural solar spectral irradiance from 360 to 800 nm. The system generates the spectral irradiance by a combination of 23 different types of LED. The irradiance of each of the 23 different LED types can be separately controlled by software to modulate the spectra. In total, the system comprises 2,530 high-power LEDs mounted on 100 printed circuit boards (PCBs) / aluminum boards. With this system, an experimental area of one square meter can be homogeneously irradiated (irradiance with a mean variability of 2 % in the integrated range of 360 nm - 800 nm) at the distance of 1.6 m simulating the spectral irradiance of the standard reference spectrum of the American Society for Testing and Materials (ASTM G173-03). At maximum, the LED lighting field can reach an irradiance of 2,500 W m-2, which is more than twice than that of the brightest sunlight in Central Europe. Thus, the new system opens up multiple new applications in many research areas ranging from photobiology to human health and environmental and material sciences.