Abstract: An image segmentation algorithm based on Geometric Active Contour（GAC） model and fractional box-counting dimension is presented in order to solve the problem that tradition GAC model can’t segment adaptively and this kind of model usually leaks boundary and needs long time’s evolution.This algorithm combines image information（fractional box-counting dimension of image） and curve location.In this algorithm，evolution speed v(D) which depends on fractional box-counting dimension of inward and outward area’s of curve replaced constant speed v in tradition GAC model.Experimental results show that the proposed algorithm is feasible，reduces segmentation time and reaches an obvious effect in terms of boundary leaking.