Application of biometric identification systems is one of the most trustable ways to control the access of users to real and virtual spaces. The use of unique features such as finger print, face, iris, retina, palm, voice and signature is common in biometric identification systems. Due to ease and speed, in this thesis voice-based verification system is studied. Speaker verification systems can be used to secure the access of authorized users to places, in organizations such as banks and insurance companies, refineries and power-plants control centers, strategic research laboratories and even hospitals, also to control the access to information and services from short or long-distance. Preprocessing and speaker modeling are two essential parts of speaker verification systems, in which preprocessing consists of feature extraction and feature selection. In this thesis Mel-frequency cepstral coefficients are used as feature vectors and Ant Colony Optimization (ACO) algorithm is used for feature selection. This algorithm has not been used in speaker verification systems so far. Then Gaussian Mixture Model (GMM) is used to model the speakers which is one of the most common methods for modeling feature vectors extracted from speech signals. The proposed method may be deployed for improving text independent speaker verification using ACO algorithm and GMM for speaker modeling (ACO-GMM). TIMIT data set is used to evaluate the system. Implementation results on this data set shows that use of this system will improve performance and decrease decision time of the system.