Planning has been a cornerstone of artificial intelligence for solving complex problems, and recent progress in LLM-based multi-agent frameworks have begun to extend this capability. However, the role of human-like memory within these frameworks remains largely unexplored. Understanding how agents coordinate through memory is critical for natural language planning, where iterative reasoning, constraint tracking, and error correction drive the success. Inspired by working memory model in cognitive psychology, we present EvoMem, a multi-agent framework built on a dual-evolving memory mechanism. The framework consists of three agents (Constraint Extractor, Verifier, and Actor) and two memory modules: Constraint Memory (CMem), which evolves across queries by storing task-specific rules and constraints while remains fixed within a query, and Query-feedback Memory (QMem), which evolves within a query by accumulating feedback across iterations for solution refinement. Both memory modules are reset at the end of each query session. Evaluations on trip planning, meeting planning, and calendar scheduling show consistent performance improvements, highlighting the effectiveness of EvoMem. This success underscores the importance of memory in enhancing multi-agent planning.