Abstract: A new partial differential equation model is proposed for document image binarization with multiplicative noise. The model contains data fidelity term, binary classification term and regularization term, in which the former two terms are weighted by introduction of edge stop function, making them adaptive to the original image according to its own characteristics of the fidelity or binarization of the original image, while the regularization term is used to suppress multiplicative noise. The model is solved numerically by explicit finite difference method, and many typical document images in DIBCO public data set are tested. Experimental results show that the proposed model is effective for binarization of document images with multiplicative noise, and gives the best binarization performance on the whole when compared with other relevant methods.