Solving problems often requires seeing new connections between concepts or events that seemed unrelated at first. Innovative solutions of this kind depend on analogical reasoning, a relational reasoning process that involves mapping similarities between concepts. Brain-based evidence has implicated the frontal pole of the brain as important for analogical mapping. Separately, cognitive research has identified semantic distance as a key characteristic of the kind of analogical mapping that can support innovation (i.e., identifying similarities across greater semantic distance reveals connections that support more innovative solutions and models). However, the neural substrates of semantically distant analogical mapping are not well understood. Here, we used functional magnetic resonance imaging (fMRI) to measure brain activity during an analogical reasoning task, in which we parametrically varied the semantic distance between the items in the analogies. Semantic distance was derived quantitatively from latent semantic analysis. Across 23 participants, activity in an a priori region of interest (ROI) in left frontopolar cortex covaried parametrically with increasing semantic distance, even after removing effects of task difficulty. This ROI was centered on a functional peak that we previously associated with analogical mapping. To our knowledge, these data represent a first empirical characterization of how the brain mediates semantically distant analogical mapping.