At present, Chinese data element market construction has entered a period of rapid development, which has become an important part of promoting the development of socialist market economy and deepening the reform of factor marketization. Competition mechanism is one of the basic mechanisms of market economy. The realization of the core connotation of high-quality development of data element markets needs the promotion of competition mechanism. However, there are problems in the operation of China’s data element markets at present in enterprise （operator） behavior, market structure and state （government） intervention: Firstly, the new unfair competition and monopoly behavior of enterprises in data element markets have an impact on the market competition order; secondly, the construction of regional data trading platform has the possibility of cutting off the regional market; thirdly, the government’s improper intervention in data element markets is likely to breed administrative monopoly. Therefore, how to maintain the competition order of data element markets according to its own characteristics, and then realize the scientific and efficient data circulation, has become an urgent problem to be solved. Therefore, we should solve the problems in three aspects, and promote the establishment of benign competition ecosystem of data element markets: Firstly, for the new types of unfair competition and monopoly behavior in data element markets, we should promote the identification standard of unfair competition behavior, the relevant market definition of monopoly behavior and the improvement of anti-competitive effect evaluation system, so as to build a dynamic, flexible and efficient system of competition law; secondly, we should speed up the construction of domestic unified data element markets, break the regional market barriers, and promote the construction of national data element markets, so as to realize the cross regional flow of data; thirdly, for the problem of administrative monopoly in the process of data element market construction, we should strengthen the standardization of government administrative behavior, implement the fair competition review system, improve or abolish the policies that have a negative impact on competition, accelerate the promotion of government data opening, and improve the quantity and quality of government data opening, so as to avoid the improper interference of administrative power from damaging the competition mechanism. Through the solution of the three problems, we should coordinate the interests of various parties and balance the needs of multiple values, create a scientific and reasonable competition order in data element markets, promote the effective competition , and create a data element markets.