Improvements in technology have triggered the production of big data. Within this scope, enormous amounts of biological data have been generated. A number of analysis methods have been developed to access the information contained in biological data. DNA sequence analysis has drawn particular attention in recent years. As an alternative to alignment-based sequence comparison methods that have high computational costs, alignment-free comparison methods have emerged. These methods can calculate sequence similarity by applying different dimensions of numerical characterizations. In this paper, we propose a novel alignment-free DNA sequence analysis method based on a feature extraction strategy. The method utilizes numerical characterization and is implemented by calculating mean distance of the transitions, mean distance of the nucleotide duplications, and the base frequencies. The method then measures the similarity between 7-dimensional vectors that are obtained through feature extraction. Using this approach, we conducted a sequence similarity analysis of two different DNA sequence datasets of different lengths to demonstrate the effectiveness of the method. The proposed method shows that a simple and successful feature vector can be obtained when DNA sequences having many properties are used in combination with appropriate and effective descriptors. With this strategy, reasonable results were obtained with a low computational cost.