Many sensory systems (e.g., vision and hearing) show a response that is proportional to the fold-change in the stimulus relative to the background, a feature related to Weber's Law. Recent experiments suggest such a fold-change detection feature in signaling systems in cells: a response that depends on the fold-change in the input signal, and not on its absolute level. It is therefore of interest to find molecular mechanisms of gene regulation that can provide such fold-change detection. Here, we demonstrate theoretically that fold-change detection can be generated by one of the most common network motifs in transcription networks, the incoherent feedforward loop (I1-FFL), in which an activator regulates both a gene and a repressor of the gene. The fold-change detection feature of the I1-FFL applies to the entire shape of the response, including its amplitude and duration, and is valid for a wide range of biochemical parameters.