The Balloon Analogue Risk Task (BART) is a popular task used to measure risk-taking behavior. To identify cognitive processes associated with choice behavior on the BART, a few computational models have been proposed. However, the existing models are either too simplistic or fail to show good parameter recovery performance. Here, we propose a novel computational model, the exponential weight updating (EU) model that addresses the limitations of existing models. By using multiple model comparison methods including post-hoc model fits criterion and parameter recovery, we showed that the EU model outperforms the existing models. In addition, we applied the EU model to BART data from healthy controls and substance-using populations (patients with past opiate and stimulant dependence). The modeling results suggest that heroin users show increased risk preference and reduced loss aversion than other groups.