This paper presents an explore-and-classify framework for structured architectural reconstruction from an aerial image. Starting from a potentially imperfect building reconstruction by an existing algorithm, our approach 1) explores the space of building models by modifying the reconstruction via heuristic actions; 2) learns to classify the correctness of building models while generating classification labels based on the ground-truth, and 3) repeat. At test time, we iterate exploration and classification, seeking for a result with the best classification score. We evaluate the approach using initial reconstructions by two baselines and two state-of-the-art reconstruction algorithms. Qualitative and quantitative evaluations demonstrate that our approach consistently improves the reconstruction quality from every initial reconstruction.