Vision-language navigation in unknown environments is crucial for mobile robots. In scenarios such as household assistance and rescue, mobile robots need to understand a human command, such as "find a person wearing black". We present a novel vision-language navigation (VL-Nav) system that integrates efficient spatial reasoning on low-power robots. Unlike prior methods that rely on a single image-level feature similarity to guide a robot, we introduce the heuristic-vision-language (HVL) spatial reasoning for goal point selection. It combines pixel-wise vision-language features and heuristic exploration to enable efficient navigation to human-instructed instances in various environments robustly. We deploy VL-Nav on a four-wheel mobile robot and conduct comprehensive navigation tasks in various environments of different scales and semantic complexities, indoors and outdoors. Remarkably, VL-Nav operates at a real-time frequency of 30 Hz with a Jetson Orin NX, highlighting its ability to conduct efficient vision-language navigation. Experimental results show that VL-Nav achieves an overall success rate of 86.3%, outperforming previous methods by 44.15%.