Digital image halftoning is a widely used technique. However, achieving high fidelity tone reproduction and structural preservation with low computational time cost remains a challenging problem. This paper presents a highly parallel algorithm to boost real-time application of serial structure-preserving error diffusion. The contrast-aware halftoning approach is one such technique with superior structure preservation, but it offers only a limited opportunity for graphics processing unit(GPU) acceleration. Our method integrates contrast-aware halftoning into a new parallelizable error-diffusion halftoning framework. To eliminate visually disturbing artifacts resulting from parallelization, we propose a novel multiple quantization model and space-filling curve to maintain tone consistency, blue-noise property, and structure consistency. Our GPU implementation on a commodity personal computer achieves a real-time performance for a moderately sized image. We demonstrate the high quality and performance of the proposed approach with a variety of examples, and provide comparisons with state-of-the-art methods.