Ultrasound imaging has huge importance for medical diagnosis because of it being a non-invasive technique and can give a real time image. Nevertheless, speckle noise in ultrasound images considerably degrades their quality and renders them non diagnostic. In this paper a fuzzy based adaptive filter is proposed for speckle noise reduction in ultrasound images while retaining important structure of speckle noise. Logarithmic transformation is used to linearize multiplicative noise, and it uses adaptive fuzzy membership functions to identify and suppress noisy pixels. Noisy pixels are corrected with a fuzzy weighted average of surrounding pixels and a median filter is then used for post processing to remove any residual noise entrainment artifacts. The proposed method is quantitatively evaluated using PSNR, IDPC, EPI and ENL image quality metrics. The use of the proposed filter yields better noise suppression, edge preservation and detail retention than Lee and Frost filters according to experimental results. There is a great potential of the presented technique for medical imaging, remote sensing, and document restoration applications.