New text independent speaker identification method is presented. Phase spectrum of all-pole linear prediction (LP) model is used to derive the speech features. The features are represented by pairs of numbers that are calculated from group delay extremums of LP model spectrum. The first component of the pair is an argument of maximum of group delay of all pole LP model spectrum and the second is an estimation of spectrum bandwidth at the point of spectrum extremum. A similarity metric that uses group delay features is introduced. The metric is adapted for text independent speaker identification with general assumption that test speech channel may contain multiple speakers. It is demonstrated that automatic speaker recognition system with proposed features and similarity metric outperforms systems based on Gaussian mixture model with Mel frequency cepstral coefficients, formants, antiformants and pitch features.