The development of Large Language Models (LLMs) enables LLM-based GUI testing to interact with graphical user interfaces by understanding GUI screenshots and generating actions, which are widely applied in industry and academia. However, current approaches test each app in isolation, lacking mechanisms for experience accumulation and reuse. This limitation often causes GUI testing approaches to miss deeper exploration and fail to trigger bug-prone functionalities. To address this, we propose MemoDroid, a three-layer memory mechanism that augments LLM-based GUI testing with the ability to evolve through repeated interaction. MemoDroid designs episodic memory to capture functional-level testing traces, reflective memory to summarize failure patterns and redundant behaviors, and strategic memory to synthesize cross-app exploration strategies. These memory layers are dynamically retrieved and injected into LLM prompts at runtime, enabling the agent to reuse successful behaviors, avoid ineffective actions, and prioritize bug-prone paths. We implement MemoDroid as a lightweight plugin, which can be integrated into existing LLM-based GUI testing approaches. We evaluate MemoDroid on real-world apps from 15 diverse categories. Results show that MemoDroid enhances GUI testing performance across five baseline methods, with activity and code coverage increasing by 79% - 96% and 81% - 97%, and bug detection improving by 57% - 198%. Ablation studies confirm the contributions of each memory layer. Furthermore, MemoDroid detects 49 new bugs in 200 real-world apps, with 35 confirmed fixes and 14 acknowledged by developers, showing its practical value in memory-driven GUI testing.