In this contribution we propose an a priori signal-to-noise ratio (SNR) estimator based on a probabilistic speech model. Since the a priori SNR is an important means for speech enhancement algorithms, such as weighting rule calculation for noise reduction or speech presence probability computation, its diligent estimation is of wide interest. As a basis for this estimator a Gaussian mixture model (GMM) is trained on clean speech amplitudes and by finding the maximum likelihood (ML) clean speech estimate of the corresponding observed frame the a priori SNR can easily be calculated. Additionally, an iterative scheme is applied to consequently enhance the estimate by repetitively evaluating the GMM. This technique allows to accomplish noise reduction free of musical tones even in non-stationary noise environments and exceeds the quality of the classical decision-directed (DD) approach for typical spectral weighting rules.