With the exponential growth of genomic sequences, there is an increasing demand to accurately identify protein coding regions (exons) from genomic sequences. Despite many progresses being made in the identification of protein coding regions by computational methods during the last two decades, the performances and efficiencies of the prediction methods still need to be improved. In addition, it is indispensable to develop different prediction methods since combining different methods may greatly improve the prediction accuracy. A new method to predict protein coding regions is developed in this paper based on the fact that most of exon sequences have a 3-base periodicity, while intron sequences do not have this unique feature. The method computes the 3-base periodicity and the background noise of the stepwise DNA segments of the target DNA sequences using nucleotide distributions in the three codon positions of the DNA sequences. Exon and intron sequences can be identified from trends of the ratio of the 3-base periodicity to the background noise in the DNA sequences. Case studies on genes from different organisms show that this method is an effective approach for exon prediction.