The paper is dealing with the world nuclear energy development trends and Russia's competitiveness at the global nuclear market. The problems of energy supply and energy security are among the most urgent in the modern world economy. The modern nuclear market consists of the natural uranium market, uranium conversion and enrichment services, nuclear fuel, the nuclear power engineering market, the electricity and capacity market, the market nuclear power plants construction and service. At all those specific markets Russia is competing with the number of developed nations and China. The regional development global nuclear market is based on diversification. Many new real and potential importers are emerging in Asia, Latin America and Africa. Russia needs a whole range of measures to strengthen its competitiveness, production and processing of nuclear fuel, nuclear technology, training highly skilled personnel. The authors are evaluating the level of Russian nuclear energy industry and its major company "Rosatom" competitiveness.