This paper presents Maximum A Posteriori (MAP) estimation of the spectral components of clean speech from the observed data noised by the additive background noise having Gaussian or non-Gaussian statistical distribution. In the proposed algorithm MAP estimator for the spectral components of clean signal is derived using Generalized Gaussian Distribution (GGD) function as a priori statistical models for the spectral components of speech as well as noise. Since the spikiness of the GGD can be controlled by the shape parameter, it is possible to model Gaussian as well as non-Gaussian noise, corrupting the speech signal. The enhancement results for the speech signal corrupted by the Gaussian noise and non- Gaussian noise are presented to show the usefulness of the estimator. Denoising performance for the Laplacian noise and white Gaussian noise have also been compared with that of the conventional Wiener filtering, which assumes Gaussian distributions for both the speech and noise.