Dynamic, momentary affective states have significant effects on creativity; however, how negative affect modulates the neurocognitive processes involved in creativity is still unclear. This study investigated the neural mechanisms of creative thinking under varying avoidance-motivation intensity. Sixty participants (17 men and 43 women; age range = 18-25 years; mean = 21.22 years, SD = 1.35) randomly assigned to three groups (high-avoidance-motivation, low-avoidance-motivation, and unmotivated bias state) completed creative tasks in two conditions -- creative idea generation and creative idea evaluation. In the former condition, the low-avoidance-motivation group exhibited greater fluency of divergent thinking than the high-avoidance-motivation group. Functional near-infrared spectroscopy revealed an interaction effect between creative demand and avoidance-motivation intensity in the bilateral inferior frontal gyrus and right middle frontal gyrus in creative idea generation. In the latter condition, there were no significant differences between the three avoidance motivation groups in behavior and brain activation results. Furthermore, the association of the prefrontal cortex and temporal region in these tasks indicated that these regions may be part of the core mechanism underlying the modulatory effects of avoidance-motivation intensity on ongoing neurocognitive processing during creative thinking.