In this letter, we propose a new level-set-based energy functional for the purpose of synthetic aperture radar (SAR) image segmentation into Gamma homogeneous regions. The segmentation of SAR images is a difficult problem due to the presence of speckles, which can be modeled as strong multiplicative noise. Our proposed energy functional is designed to get a stationary global minimum. As a result, the level set function that evolves by the Euler-Lagrange equation of the energy functional has a unique stationary convergence state. Moreover, it is easy to set a termination criterion on the curve evolution via a level set by using our energy functional. The experimental results on both synthetic and real SAR images demonstrate the effectiveness of our method.