Generalized Nekrasov matrices, also known as nonsingular H-matrices, have a wide range of applications. Judging whether a matrix is a generalized Nekrasov matrix is an important research topic, which has attracted the attention of a large number of scholars. In this paper, two new criteria for generalized Nekrasov matrices are proposed. By constructing a positive diagonal matrix with diagonal elements less than or equal to 1, the lower triangle part of Nekrasov sum was reduced and then the new criteria improved several existing results. In order to further illustrate the results proposed in this paper, four numerical examples are designed in the last section. The numerical examples show that each of two new criteria can be better than the other one and both are weaker than some existing conditions. The method of reducing the lower triangle part of Nekrasov sum provides a new idea for the discrimination of generalized Nekrasov matrices.