The emerging computing paradigms offer effective resolutions for the escalating conflict arising from the heightened computational demands of portable terminals and their constrained capacity. Concurrently, the architecture has transitioned from a single-tier structure to a multi-tier collaborative framework, enhancing flexibility and enabling fine-grained computation offloading. Nevertheless, existing research on multi-tier computation offloading faces challenges, including inefficient resource perception and task decomposition; there is a notable absence of an effective hierarchical task scheduling strategy within the multi-tier collaborative architecture. To bridge these gaps, our article investigates the multi-granularity task decomposition and hierarchical task scheduling in a cloud-edge-end collaborative computing network. We first introduce a large-small resource tree (LST) model to facilitate efficient resource perception across three-tier network nodes. Then we propose a multi-granularity task decomposition algorithm (MTDA) based on long short-term memory (LSTM) network resource prediction to fully utilize the distributed node resources. Finally, we propose a parallelized LST-DDQN task offloading algorithm to maximize the delay and energy consumption weighted utility function. Simulation results demonstrate the efficacy of our proposed task decomposition and parallel scheduling methods, showcasing a reduction in utility by approximately 6.31% to 13.01% compared to baseline algorithms.