•We propose a strict convex variational level set model for document binarization, and it has a unique global minimizer.•It is an initialization-flexible model, and the evolution termination condition can be set via level set function.•Our model can deal with many kinds of degradations, such as, low contrast, bleed-through, faint characters, texture.•Our model can achieve comparable or better performance. Moreover, it is efficient and robust to noise to some extent. Document image binarization is a significant stage in the optical character recognition system. Different from previous binarization approaches, in this paper, we propose a novel and convex variational level set model for document image binarization. Our energy functional is comprised of two terms: data term and fidelity term. We prove that our model is strictly convex and has a unique global minimum solution, which enables us to set the evolution termination criterion by the normalized step difference energy that measures the convergence state of level set function. We experimentally demonstrate the advantage of the fidelity term and show the merit of level set initialization robustness. In addition, the convergence of the alternative minimization algorithm for solving our model is analyzed. Extensive experiments are conducted on JM dataset, representative degraded document images and DIBCO series datasets to evaluate our model qualitatively and quantitatively. The experiment results verify that our model is effective to deal with most kinds of degraded images. Compared with four evolution and six non-evolution based binarization methods, our model could achieve better or competitive performance in terms of four metrics.