A fast and accurate panoptic segmentation system for LiDAR point clouds is crucial for autonomous driving vehicles to understand the surrounding objects and scenes. Existing approaches usually rely on proposals or clustering to segment foreground instances. As a result, they struggle to achieve real-time performance. In this paper, we propose a novel real-time end-to-end panoptic segmentation network for LiDAR point clouds, called CPSeg. In particular, CPSeg comprises a shared encoder, a dual decoder, a task-aware attention module (TAM) and a cluster-free instance segmentation head. TAM is designed to enforce these two decoders to learn rich task-aware features for semantic and instance embedding. Moreover, CPSeg incorporates a new cluster-free instance segmentation head to dynamically pillarize foreground points according to the learned embedding. Then, it acquires instance labels by finding connected pillars with a pairwise embedding comparison. Thus, the conventional proposal-based or clustering-based instance segmentation is transformed into a binary segmentation problem on the pairwise embedding comparison matrix. To help the network regress instance embedding, a fast and deterministic depth completion algorithm is proposed to calculate surface normal of each point cloud in real-time. The proposed method is benchmarked on two large-scale autonomous driving datasets, namely, SemanticKITTI and nuScenes. Notably, extensive experimental results show that CPSeg achieves the state-of-the-art results among real-time approaches on both datasets.