Fluctuations in signed distance measurement often reduce the numerical precision of level set methods (LSMs) in image segmentation. Inspired by the split Bregman method for L1-regularization problems, this paper proposes an efficient energy-based level set framework with Bregman divergence reaction to achieve stable and accurate numerical solutions. In this proposed algorithm, the level set and its signed distance function (SDF) are formulated as a constrained L1-norm optimization problem. Bregman divergence is then introduced as a new energy measurement of the level set function. By adding the reaction term for the divergence, SDF with L1-norm constraint is then computed under an unconstrained optimization framework. Efficient numerical algorithms such as Fast Fourier Transformation (FFT) and Newton's method are further adopted within a unified computational framework for solving the sub-minimizations. Extensive experimental results demonstrate that the proposed level set algorithm is able to achieve competitive performance in medical image segmentation.