We propose a novel approach for noise-robust speaker recognition, where the model of distortions caused by additive and convolutive noises is integrated into the i-vector extraction framework. The model is based on a vector taylor series (VTS) approximation widely successful in noise robust speech recognition. The model allows for extracting ”cleaned-up” i-vectors which can be used in a standard i-vector back end. We evaluate the proposed framework on the PRISM corpus, a NIST-SRE like corpus, where noisy conditions were created by artificially adding babble noises to clean speech segments. Results show that using VTS i-vectors present significant improvements in all noisy conditions compared to a state-of-theart baseline speaker recognition. More importantly, the proposed framework is robust to noise, as improvements are maintained when the system is trained on clean data.