In this paper, for effectively computing the similarity between DNA sequences, we introduce a novel method based on frequency patterns and entropy to construct representative vectors of DNA sequences. Experiments are conducted to evaluate the proposed method, which is compared with two recently-developed alignment-free methods and the BLASTN tool. When testing on the β-globin genes of 11 species and using the results from MEGA as the baseline, our method achieves higher correlation coefficients than the two alignment-free methods and the BLASTN tool.