Enabling robots to navigate following diverse language instructions in unexplored environments is an attractive goal for human-robot interaction. However, this goal is challenging because different navigation tasks require different strategies. The scarcity of instruction navigation data hinders training an instruction navigation model with varied strategies. Therefore, previous methods are all constrained to one specific type of navigation instruction. In this work, we propose InstructNav, a generic instruction navigation system. InstructNav makes the first endeavor to handle various instruction navigation tasks without any navigation training or pre-built maps. To reach this goal, we introduce Dynamic Chain-of-Navigation (DCoN) to unify the planning process for different types of navigation instructions. Furthermore, we propose Multi-sourced Value Maps to model key elements in instruction navigation so that linguistic DCoN planning can be converted into robot actionable trajectories. With InstructNav, we complete the R2R-CE task in a zero-shot way for the first time and outperform many task-training methods. Besides, InstructNav also surpasses the previous SOTA method by 10.48% on the zero-shot Habitat ObjNav and by 86.34% on demand-driven navigation DDN. Real robot experiments on diverse indoor scenes further demonstrate our method's robustness in coping with the environment and instruction variations.