Digital halftoning is a technique for converting a continuous-tone image into a quantized image to reproduce it on a digital printing device. Error diffusion (ED) is an algorithm that has proven to be effective for the halftoning process, and it has been widely applied to digital printing tasks. However, in images reproduced using conventional ED algorithms based on the signal processing theory, the texture of objects is often lost. In this study, we propose a texture-aware ED algorithm for multi-level digital halftoning. First, we generate multiple mapped images with different brightness levels through nonlinear transformation. For each mapped image, we adopt a texture-aware binary error diffusion method to obtain multiple halftone images. Finally, we generate a multi-level halftone image from the multiple halftone images. We test the algorithm on an actual printer, compare the results with those of the current raster image processor software and classical ED algorithms, and observe that our algorithm outputs better results.