The use of tunable light sources is more and more common in laboratories but also in everyday lives. Multi-channel LED light sources in laboratories are able to mimic and produce spectral distributions of different light sources so even different CIE standard illuminants now become realizable by an artificial source. The tunable light source can also be very important to mimic changing spectral distributions of daylight throughout the day. The purpose of my master thesis was to find the mathematical method, which calculates optimal synthesized spectrum with a help of multiple LEDs, as close to the wanted (target) spectrum as possible. Three different methods that are described and tested in the thesis are based on a Gauss optimization method. These methods calculate a coefficient or a current for each LED, as to find a right combination of LEDs coefficients to synthesize six different wanted spectrums. Two different LED sets were used in the calculations, which were integrated into a sphere. The optimization method was used in practice with an existing tunable color light source based on LEDs, which was driven by a program written in LabVIEW environment. Few problems were found with the implementation of the optimal method into the program, which were successfully resolved. Problems accrued because of the characteristics of the LEDs and because of small values of coefficients, which must be large enough; only then can the tunable color light source be fully used. With the tested tunable color light source we were able to produce all six tested target spectrums in practice, which had all parameters close to the target spectrum, which was also the purpose of the thesis.