In this paper,we propose a new 4D graphical representation of DNA primary sequences based on the Z-curve theory.The advantage of our approach is that it has the similar biological significance with the Z-curve,and it does not lose any biological information of the sequence.The geometrical centers of the 4D graphical representation of DNA sequences are used as the numerical characterizations,and the examination of similarities/dissimilarities about the coding sequences of the first exon of β-globin genes of eleven different species shows that this approach can provide satisfactory results.