In this paper, we propose a coding algorithm for High Dynamic Range Images (HDRI). Our encoder applies a tone mapping model based on scaled µ-Law encoding, followed by a conventional Low Dynamic Range Image (LDRI) encoder. The tone mapping model is designed to minimize the difference between the tone-mapped HDRI and its LDR version. By virtue of the nature of the µ-Law model, not only the quality of the HDRI but also the one of the LDRI is improved, compared with a state of the art in conventional HDRI coding methods. Furthermore the error limit caused by our encoding is theoretically analyzed.