A central goal of synthetic biology is to apply successful principles that have been developed in electronic and chemical engineering to construct basic biological functional modules, and through rational design, to build synthetic biological systems with predetermined functions. Here, we apply the reverse engineering design principle of biological networks to synthesize a gene circuit that executes semi-log dose-response, a logarithmically linear sensing function, in Escherichia coli cells. We first mathematically define the object function semi-log dose-response, and then search for tri-node network topologies that can most robustly execute the object function. The simplest topology, transcriptional coherent feed-forward loop (TCFL), among the searching results is mathematically analyzed; we find that, in TCFL topology, the semi-log dose-response function arises from the additive effect of logarithmical linearity intervals of Hill functions. TCFL is then genetically implemented in E. coli as a logarithmically linear sensing biosensor for heavy metal ions [mercury (II)]. Functional characterization shows that this rationally designed biosensor circuit works as expected. Through this study we demonstrated the potential application of biological network reverse engineering to broaden the computational power of synthetic biology.