Live-scanning devices are widely used in many fields. An important difference between fingerprint images acquired by ink and paper and fingerprints acquired by live-scanning devices is completeness. Since the sensor sizes of live-scanning devices are usually smaller than an average fingerprint and users may not align their fingers properly on the sensors, only a part of a fingerprint may be scanned, resulting in the omission of some singular points. In this paper, we propose a novel approach which increases the classification performance for fingerprint images obtained by live-scanning devices. We extract ridge directional values and create Markov models. However, Markov models in each class share most transitions because fingerprints are basically circular in shape. In order to enhance the specific transitions of each class and to suppress the common transitions in the Markov models, we apply genetic algorithms. The performance of the optimized classification model using genetic algorithms was shown to be superior to the pre-optimization model. The proposed method effectively classifies live-scanned fingerprint images because this approach is based on the global feature of ridge direction, and is independent of the existence of singular points.