Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 \& 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at https://github.com/opendilab/SmartRefine/.