This paper introduces a novel approach to improve performance of speech recognition systems using a combination of features obtained from speech reconstructed phase space (RPS) and frequency domain analysis. By choosing an appropriate value for the dimension, reconstructed phase space is assured to be topologically equivalent to the dynamics of the speech production system, and could therefore include information that may be absent in analysis approaches based on linear methods. Also, complicated systems such as speech production system can present cyclic and oscillatory patterns and Poincare sections could be used as an effective tool in analysis of such trajectories. In this research, a statistical modeling approach based on Gaussian Mixture models (GMM) was applied to the Poincare sections of speech RPS. The final feature set is obtained from a feature selection stage omong parameters of GMM model and the usual Mel Frequency Cepstral coefficients (MFCC). An HMM-based speech recognition system and the TIMIT speech database are used to evaluate performance of the proposed feature extraction system for isolated and continuous speech recognition. Experiments represent about 5.7% absolute isolated phoneme recognition accuracy improvement in isolated phoneme recognition performance. The new approach is shown to be a viable and effective alternative to traditional feature extraction methods, particularly for signals such as speech with strong nonlinear characteristics.