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We propose VLM-Social-Nav, a novel Vision-Language Model (VLM) based navigation approach to compute a robot's motion in human-centered environments. Our goal is to make real-time decisions on robot actions that are socially compliant with human expectations. We utilize a perception model to detect important social entities and prompt a VLM to generate guidance for socially compliant robot behavior. VLM-Social-Nav uses a VLM-based scoring module that computes a cost term that ensures socially appropriate and effective robot actions generated by the underlying planner. Our overall approach reduces reliance on large training datasets and enhances adaptability in decision-making. In practice, it results in improved socially compliant navigation in human-shared environments. We demonstrate and evaluate our system in four different real-world social navigation scenarios with a Turtlebot robot. We observe at least 27.38% improvement in the average success rate and 19.05% improvement in the average collision rate in the four social navigation scenarios. Our user study score shows that VLM-Social-Nav generates the most socially compliant navigation behavior.