Many believe that project complexity reduces project management performance. However, so far research has failed to establish this causal relationship conclusively. We extend research on project complexity by introducing the concept of team-level absorptive capacity and by studying its role as mediator between project complexity and project management success. Applying structural equation modelling to a sample of 285 respondents, we find an unequivocal, direct and positive statistical association between project complexity and delays and overspending. Further, we show that team-level absorptive capacity is critical for successful project management, but also that absorptive capacity can only partially offset the harmful impact of project complexity. Beyond adding to project management theory, the paper contributes to the wider management literature. We establish complexity as an antecedent of absorptive capacity and demonstrate how each dimension of absorptive capacity has unique determinants and outcomes. •Project complexity increases the risk of unscheduled delays.•Project complexity makes cost overruns more likely.•Team-level absorptive capacity mitigates delays and overspending.•Project-team capacities cannot fully offset the effect of project complexity.