This paper presents a new beamforming method for ultrasound medical imaging based upon the statistical characterization of the ultrasound signals by α-stable distributions. The proposed method was evaluated on ultrasound simulated and in vivo thyroid data. In simulation, an improvement in contrast ratio of 2.84 dB, 11.52 dB, and 13.33 dB was obtained compared with minimum variance, delay-and-sum, and least squares beamformers respectively. Applied on in vivo data and compared to delay-and-sum and least squares, our method increases the contrast ratio between the tumor and the healthy tissue by 1.28 dB, respectively 1.54 dB.