This paper presents a robust speaker identification method from degraded speech signals. This method is based on the Mel-frequency cepstral coefficients (MFCCs) for feature extraction from the degraded speech signals and the wavelet transform of these signals. It is known that the MFCCs based speaker identification method is not robust enough in the presence of noise and telephone degradations. So, the feature extraction from the wavelet transform of the degraded signals adds more speech features from the approximation and detail components of these signals which assist in achieving higher identification rates. Neural Networks are used in the proposed method for feature matching. The Comparison study between the proposed method and the traditional MFCCs based feature extraction method from noisy speech signals and telephone degraded speech signals with additive white Gaussian noise (AWGN) and colored noise shows that the proposed method improves the recognition rates computed at different degradation cases.