Modern detectors commonly employ classification scores to reflect the localization quality of detection results. However, there exists an inconsistency between them, misguiding the selection of high-quality predictions and providing unreliable results for downstream applications. In this paper, we find that the root of this confidence inconsistency lies in the inaccurate IoU estimation and the spatial misalignment of the learned features between the classification and localization tasks. Therefore, a Confidence-Consistent Detector (CCDet) which includes the Distribution-based IoU Prediction (DIP) and Consistency-aware label assignment (CLA), is proposed. DIP provides more stable and accurate IoU estimation by learning the probability distribution over the IoU range and employing the expectation as the predicted IoU. CLA adopts both the prediction performance and consistency degree of samples as assignment metrics to select positives, which guides the classification and localization tasks to promote similar feature distribution. Comprehensive experiments demonstrate that CCDet can effectively mitigate the confidence inconsistency between classification and localization, and achieve stable improvement across different baselines. On the test-dev set of MS COCO, CCDet acquires a single-model single-scale AP of 50.1%, surpassing most of the existing object detectors.