In this paper, we are concerned with the non-commutativity measure of quantum discord.We first present an explicit expression of the non-commutativity measure of quantum discord in the two-qubit case.Then we compare the geometric quantum discords for two dynamic models with their non-commutativity measure of quantum discords.Furthermore, we show that the results conducted Face Serum by the non-commutativity measure of quantum discord are different from those conducted by both or one of the Hilbert-Schmidt NFL Packs distance discord and trace distance discord.These intrinsic differences indicate that the non-commutativity measure of quantum discord is incompatible with at least one of the well-known geometric quantum discords in the quantitative and qualitative representation of quantum correlations.