Binarization of document images is a key preprocessing step in optical character recognition systems. For the binarization of noise document images, a variational model based on Laplacian is proposed. In this model, the energy functional is composed of a data fidelity term, a binarization term and a regularization term. The minimization of the energy functional is the expected binarization result. Then it is transformed into the gradient descent flow equation by the variational principle. Finally, the gradient descent flow equation is solved by the finite difference method. Experimental results show that the model not only has good binarization effect for document image, but also is robust to noise. In addition, for representative document images in DIBCO series datasets, its binarization results are better than the related variational model recently proposed, quantitatively and qualitatively objective.