Recent advancements in Large Language Model(LLM)-based Multi-Agent Systems(MAS) have demonstrated remarkable potential for tackling complex decision-making tasks. However, existing frameworks inevitably rely on serialized execution paradigms, where agents must complete sequential LLM planning before taking action. This fundamental constraint severely limits real-time responsiveness and adaptation, which is crucial in dynamic environments with ever-changing scenarios. In this paper, we propose a novel parallelized planning-acting framework for LLM-based MAS, featuring a dual-thread architecture with interruptible execution to enable concurrent planning and acting. Specifically, our framework comprises two core threads:(1) a planning thread driven by a centralized memory system, maintaining synchronization of environmental states and agent communication to support dynamic decision-making; and (2) an acting thread equipped with a comprehensive skill library, enabling automated task execution through recursive decomposition. Extensive experiments on challenging Minecraft demonstrate the effectiveness of the proposed framework.