Incidental negative emotions unrelated to the current task, such as background anxiety, can strongly influence decisions. This is most evident in psychiatric disorders associated with generalized emotional disturbances. However, the neural mechanisms by which incidental emotions may affect choices remain poorly understood. Here we study the effects of incidental anxiety on human risky decision making, focusing on both behavioral preferences and their underlying neural processes. Although observable choices remained stable across affective contexts with high and low incidental anxiety, we found a clear change in neural valuation signals: during high incidental anxiety, activity in ventromedial prefrontal cortex and ventral striatum showed a marked reduction in (1) neural coding of the expected subjective value (ESV) of risky options, (2) prediction of observed choices, (3) functional coupling with other areas of the valuation system, and (4) baseline activity. At the same time, activity in the anterior insula showed an increase in coding the negative ESV of risky lotteries, and this neural activity predicted whether the risky lotteries would be rejected. This pattern of results suggests that incidental anxiety can shift the focus of neural valuation from possible positive consequences to anticipated negative consequences of choice options. Moreover, our findings show that these changes in neural value coding can occur in the absence of changes in overt behavior. This suggest a possible pathway by which background anxiety may lead to the development of chronic reward desensitization and a maladaptive focus on negative cognitions, as prevalent in affective and anxiety disorders.