Intensity inhomogeneity brings great difficulties to image segmentation. This problem is partly solved by the multiplicative bias field correction model. However, some other problems still exist, such as slow segmentation speed and narrow application field. In this paper, an additive bias correction (ABC) model based on intensity inhomogeneity is proposed. The model divides the observed image into three parts: additive bias function, reflection edge structure function and Gaussian noise. Firstly, the local area and local clustering criterion of intensity inhomogeneity are defined. Secondly, by introducing the level set function, the local clustering criterion is transformed into an energy function based on the level set model. Finally, the structure of the estimated bias field and the reflection edge is computed through the process of minimizing the energy function while the image is segmented. In order to improve the stability of the system, a de-parameterized regularization function and an adaptive data-driven term function are designed. Compared with the traditional multiplicative model, the addition model has faster calculation speed. The proposed model can obtain ideal segmentation effect for images with intensity inhomogeneity. Experiment results show that the proposed method is more robust, faster and more accurate than traditional piecewise and multiplicative models.