Similarity is one of the key processes of DNA sequence analysis in computational biology and bioinformatics. In nearly all research that explores evolutionary relationships, gene function analysis, protein structure prediction and sequence retrieving, it is necessary to perform similarity calculations. One major task in alignment-free DNA sequence similarity calculations is to develop novel mathematical descriptors for DNA sequences. In this paper, we present a novel approach to DNA sequence similarity analysis studies using similarity calculations of texture images. Texture analysis methods, which are a subset of digital image processing methods, are used here with the assumption that these calculations can be adapted to alignment-free DNA sequence similarity analysis methods. Gray-level textures were created by the values assigned to the nucleotides in the DNA sequences. Similarity calculations were made between these textures using histogram-based texture analyses based on first-order statistics. We obtained texture features for 3 different DNA data sets of different lengths, and calculated the similarity matrices. The phylogenetic relationships revealed by our method shows our trees to be similar to the results of the MEGA software, which is based on sequence alignment. Our findings show that texture analysis metrics can be used to characterize DNA sequences.