The ability to evaluate the balance between risk and reward and to adjust behavior accordingly is fundamental to adaptive decision-making. Although brain-imaging studies consistently have shown involvement of the dorsolateral prefrontal cortex, anterior insula and striatum during risky decision-making, activation in a neural network formed by these regions has not been linked to structural connectivity. Therefore, in this study, white-matter connectivity was measured with diffusion-weighted imaging in 40 healthy research participants who performed the Balloon Analogue Risk Task, a test of risky decision-making, during fMRI. Fractional anisotropy within a network that includes white-matter pathways connecting four regions (the prefrontal cortex, insula and midbrain to the striatum) was positively correlated with the number of risky choices and total amount earned on the task, and with the parametric modulation of activation in regions within the network to the level of risk during choice selection. Furthermore, analysis using a mixed model demonstrated how relationships of the parametric modulation of activation in each of the four aforementioned regions are related to risk probabilities, and how previous trial outcomes and task progression influence the choice to take risk. The present findings provide the first direct evidence that white-matter integrity is linked to function within previously identified components of a network that is activated during risky decision-making, and demonstrate that the integrity of white-matter tracts is critical in consolidating and processing signals between cortical and striatal circuits during the decision-making process.