Background Etiological theories of addictive behavior postulate a key role for decision-making mechanisms. However, current research is lacking clear computational models for decision-making in multi-step forward planning scenarios to identify underlying mechanisms and make derived hypotheses testable. Methods We used a recently developed planning task and computational model to investigate performance, planning time and inferred forward planning parameters like planning depth and decision noise in 30 individuals diagnosed with mostly mild-to-moderate alcohol use disorder (AUD) relative to 32 healthy control participants, both sampled from the general population. Results Contrary to our hypothesis, we did not observe reduced planning depth in participants with AUD but found that participants with AUD showed a higher performance in the planning task. Group differences could be explained by planning time and general cognitive performance. Importantly, participants with AUD invested more time for planning, showed a higher correlation of planning depth with incentive value and showed lower response noise, potentially indicative of higher choice consistency. Conclusion The significant differences in planning time, moderation of planning depth by incentive value and choice consistency may reflect higher motivation and willingness to exert effort among participants with AUD compared to healthy controls. Overall, our findings do not support the notion that mild-to-moderate alcohol use disorder is associated with impairments in forward planning across multiple steps.