Modern large language models (LLMs) often struggle to dynamically adapt their reasoning depth to varying task complexities, leading to suboptimal performance or inefficient resource utilization. To address this, we introduce DynamicMind, a novel tri-mode thinking system. DynamicMind empowers LLMs to autonomously select between Fast, Normal, and Slow thinking modes for zero-shot question answering (ZSQA) tasks through cognitive-inspired prompt engineering. Our framework's core innovations include: (1) expanding the established dual-process framework of fast and slow thinking into a tri-mode thinking system involving a normal thinking mode to preserve the intrinsic capabilities of LLM; (2) proposing the Thinking Density metric, which aligns computational resource allocation with problem complexity; and (3) developing the Thinking Mode Capacity (TMC) dataset and a lightweight Mind Router to predict the optimal thinking mode. Extensive experiments across diverse mathematical, commonsense, and scientific QA benchmarks demonstrate that DynamicMind achieves superior ZSQA capabilities while establishing an effective trade-off between performance and computational efficiency.