Dynamics of the electro-optical response and relaxation time of nematic liquid crystal (NLC) cells doped with CdSe/ZnS semiconductor quantum dots (QDs) and homogeneously oriented by rubbed polyimide were investigated. The influence of nanoparticles' concentration as well as parameters of alternating electric field were shown. The optical response time decreased 1.5 time by increasing concentration of QDs up to 1.5mg/mL as it was compared with the pure LC. Applying unipolar square wave electric field to the LC cell reduces optical response time twice comparing to bipolar meander. However, we observed slowdown of the relaxation process both in case of doping NLC by nanoparticles and in case of applying unipolar square wave pulses.