We present a novel, hybrid parallel continuous collision detection (HPCCD) method that exploits the availability of multi-core CPU and GPU architectures. HPCCD is based on a bounding volume hierarchy (BVH) and selectively performs lazy reconstructions. Our method works with a wide variety of deforming models and supports self-collision detection. HPCCD takes advantage of hybrid multi-core architectures – using the general-purpose CPUs to perform the BVH traversal and culling while GPUs are used to perform elementary tests that reduce to solving cubic equations. We propose a novel task decomposition method that leads to a lock-free parallel algorithm in the main loop of our BVH-based collision detection to create a highly scalable algorithm. By exploiting the availability of hybrid, multi-core CPU and GPU architectures, our proposed method achieves more than an order of magnitude improvement in performance using four CPU-cores and two GPUs, compared to using a single CPU-core. This improvement results in an interactive performance, up to 148 fps, for various deforming benchmarks consisting of tens or hundreds of thousand triangles.