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A Bayesian approach using wavelet coefficient modeling is proposed for de-noising additive white Gaussian noise in medical magnetic resonance imaging (MRI). In a parallel acquisition process, the magnetic resonance image is affected by white Gaussian noise, which is additive in nature. A normal inverse Gaussian probability distribution function is taken for modeling the wavelet coefficients. A Bayesian approach is implemented for filtering the noisy wavelet coefficients. The maximum likelihood estimator and median absolute deviation estimator are used to find the signal parameters, signal variances, and noise variances of the distribution. The minimum mean square error estimator is used for estimating the true wavelet coefficients. The proposed method is simulated on MRI. Performance and image quality parameters show that the proposed method has the capability to reduce the noise more effectively than other state-of-the-art methods. The proposed method provides 8.83%, 2.02%, 6.61%, and 30.74% improvement in peak signal-to-noise ratio, structure similarity index, Pratt’s figure of merit, and Bhattacharyya coefficient, respectively, over existing well-accepted methods. The effectiveness of the proposed method is evaluated by using the mean squared difference (MSD) parameter. MSD shows the degree of dissimilarity and is 0.000324 for the proposed method, which is less than that of the other existing methods and proves the effectiveness of the proposed method. Experimental results show that the proposed method is capable of achieving better signal-to-noise ratio performance than other tested de-noising methods.