How to apply the effective methods of processing data to the research of constructing the matroid structure, so that the results of matroid theory can be applied to the research of data processing in more ways, is one of the problems that need to be solved in the research of matroid theory. Therefore, Galois connection, which is the basic operation in the theory of formal concept analysis that is an effective way in dealing data, is used as a bridge to give the definition of Galois context and obtain a method to establish a Galois context with a matroid. Furthermore, it finds that, under the matroid isomorphism and Galois isomorphism, there is a bijection between the family of matroids and the family of Galois contexts, and a bijection between the family of matroids and the family of Galois connections. Moreover, the relationship between matroids and Galois connections is found. This relationship is used to obtain the two methods for constructing matroids with Galois connections. Comparison with some relative known methods shows the advantages of the two methods. In addition, the biology examples show the role of the two methods in dealing the data of biological information.