Recently, several efficient context-based arithmetic coding algorithms have been developed successfully for lossless compression of error-diffused images. In this paper, we first present a novel block- and texture-based approach to train the multiple-template according to the most representative texture features. Based on the trained multiple template, we next present an efficient texture- and multiple-template-based (TM-based) algorithm for lossless compression of error-diffused images. In our proposed TM-based algorithm, the input image is divided into many blocks and for each block, the best template is adaptively selected from the multiple-template based on the texture feature of that block. Under 20 testing error-diffused images and the personal computer with Intel Celeron 2.8-GHz CPU, experimental results demonstrate that with a little encoding time degradation, 0.365 s (0.901 s) on average, the compression improvement ratio of our proposed TM-based algorithm over the joint bilevel image group (JBIG) standard [over the previous block arithmetic coding for image compression (BACIC) algorithm proposed by Reavy and Boncelet is 24%] (19.4%). Under the same condition, the compression improvement ratio of our proposed algorithm over the previous algorithm by Lee and Park is 17.6% and still only has a little encoding time degradation (0.775 s on average). In addition, the encoding time required in the previous free tree-based algorithm is 109.131 s on average while our proposed algorithm takes 0.995 s; the average compression ratio of our proposed TM-based algorithm, 1.60, is quite competitive to that of the free tree-based algorithm, 1.62.