Altered decision-making is a defining component of addiction, but there is little evidence whether these alterations affect multi-step planning in individuals with alcohol use disorder (AUD). We used a recently developed planning task in a cross-sectional approach to test the planning performance of 30 individuals diagnosed with AUD relative to 32 healthy control subjects, both sampled from the general population. To gain insight into the factors underlying behavioral performance, we inferred the parameters of a reinforcement learning agent performing rational planning, using a Bayesian inference scheme. This approach allowed us to differentiate between separate factors determining planning performance, e.g., planning depth, decision noise, and bias for certain action choices. Contrary to our hypothesis, we did not observe reduced planning depth in AUD subjects. Instead, our results show a small effect in the opposite direction: Healthy controls were slightly less efficient in the planning task. Importantly, subjects in the control group allocated less time for planning than AUD subjects, potentially indicative of motivational differences between groups. The group difference in planning depth persisted when controlling for both reaction times and general cognitive performance, albeit at a lesser magnitude. Altogether, our results do not favor the view that mild-to-moderate alcohol use disorder in general-population individuals generally involves impairments in cognitive tasks requiring forward planning across multiple steps.