This paper presents an air-void detection technique for air-coupled radar, which emits electromagnetic waves to interrogate an air-void inside a medium or between two media. The reflections from the air-medium interfaces are usually corrupted by air-coupling, antenna ringing, and internal reflections, rendering air-void detection very difficult or, in certain cases, impossible. The proposed method exploits the low-rank structure of the background clutter to suppress these nuisance signals. A variational mode decomposition model is developed to extract the backscattering at different air-medium interfaces as signal modes. Real experiments are conducted using a stepped frequency radar. The experimental results show that the proposed method can detect air-gap between two sand blocks.