Jacquard image segmentation is the linchpin of jacquard pattern design. Curve evolution model is a popular method for image segmentation. However, it cannot detect image features in the presence of noise. The Mumford-Shah model is more robust than curve evolution model to detect discontinuities under noisy environment, so it is more suitable for segmentation of noisy jacquard images. In this paper, an algorithm is presented to implement the numerical solving of the Mumford-Shah model, which combines the merits of finite element method and quasi-Newton method. First, a discrete version of the model is defined on finite element spaces over adaptive triangulation. Then an adjustment scheme for the triangulation is enforced to improve the iteration efficiency before current iteration begins. Finally, a minimization method based on quasi-Newton algorithm is applied to find the absolute minimum of the discrete model in the sense of Gamma-convergence. The proposed algorithm works well when it is applied to segment noisy jacquard images.