Speaker verification can be classified in two categories, text-dependent speaker verification and text-independent speaker verification. In this paper, we discuss text-dependent speaker verification. Text-dependent speaker verification system determines whether the sound characteristics of the speaker are equal to those of the specific person or not. In this paper we obtain the speaker data using a sound card in various noisy conditions, apply a new Hidden LMS (Least Mean Square) adaptive algorithm to it, and extract LPC (Linear Predictive Coding)-cepstrum coefficients as feature vectors. Finally, we use a competitive learning neural network for speaker verification. The proposed hidden LMS adaptive filter using a neural network reduces noise and enhances features in various noisy conditions. We construct a separate neural network for each speaker, which makes it unnecessary to train the whole network for a new added speaker and makes the system expansion easy. We experimentally prove that the proposed method improves the speaker verification performance.