The diagnosis of UltraSound (US) medical images is affected due to the presence of speckle noise. This noise degrades the diagnostic quality of US images by reducing small details and edges present in the image. This paper presents a novel method based on shearlet coefficients modeling of log-transformed US images. Noise-free log-transformed coefficients are modeled as Nakagami distribution and speckle noise coefficients are modeled as Gaussian distribution. Method of Log Cumulants (MoLC) and Method of Moments (MoM) are used for parameter estimation of Nakagami distribution and noise free shearlet coefficients respectively. Then noise free shearlet coefficients are obtained using Maximum a Posteriori (MaP) estimation of noisy coefficients. The experimental results were presented by performing various experiments on synthetic and real US images. Subjective and objective quality assessment of the proposed method is presented and is compared with six other existing methods. The effectiveness of the proposed method over other methods can be seen from the obtained results.