This work proposes the first online asymmetric semi-supervised framework, namely A-Teacher, for LiDAR-based 3D object detection. Our motivation stems from the observation that 1) existing symmetric teacher-student methods for semi-supervised 3D object detection have characterized simplicity, but impede the distillation performance between teacher and student because of the demand for an identical model structure and input data format. 2) The offline asymmetric methods with a complex teacher model, constructed differently, can generate more precise pseudo-labels, but is challenging to jointly optimize the teacher and student model. Consequently, in this paper, we devise a different path from the conventional paradigm, which can harness the capacity of a strong teacher while preserving the advantages of online teacher model updates. The essence is the proposed attention-based refinement model that can be seamlessly integrated into a vanilla teacher. The refinement model works in the divide-and-conquer manner that respectively handles three challenging scenarios including 1) objects detected in the current timestamp but with suboptimal box quality, 2) objects are missed in the current timestamp but are detected in past or future frames, 3) objects are neglected in all frames. It is worth noting that even while tackling these complex cases, our model retains the efficiency of the online teacher-student semi-supervised framework. Experimental results on Waymo show that our method outperforms previous state-of-the-art HSSDA for 4.7 on mAP (L1) while consuming fewer training resources.