This paper presents a fast multiphase segmentation model for inhomogeneous images by incorporating the multiphase formulation of the local and global intensity fitting energy model and the split Bregman method. By applying the globally convex image segmentation idea, we first define a new energy functional, which is then modified by incorporating information from the edge. A weight function that varies dynamically with the location of the image is applied to balance the weights between the local and global intensity fitting terms. The split Bregman method is then applied to minimize our energy functional much more efficiently. Our model can segment more general images accurately, especially images with inhomogeneity. We have applied our model to synthetic and real inhomogeneous images with desirable results. Numerical results demonstrate that our model is superior to the piecewise constant multiphase models and the local binary fitting model. The results obtained by our model are even more accurate than the original local and global intensity fitting energy model.