To detect small infrared targets under the condition of dense clutters, we propose a single-frame target detection algorithm based on a small bounding-box filter, which is characterized by good adaptability to the position and size of a small target. During the small target detection process, the proposed algorithm first searches for the local maximum gray pixel and then, a set of concentric bounding boxes whose center is the pixel found in the first step is constructed, and the detection thresholds of a neighboring region of this pixel are calculated based on the bounding boxes. Finally, the minimum threshold is used to detect small target pixels in the neighboring region. A fast version of the proposed algorithm is a minimum bounding-box filter, which can be implemented by dividing an image into blocks and using the mid-range and range to assess the concentration trend and dispersion of the background. Simulation and analysis results show that the proposed algorithm can achieve high detection probability and low false alarm rate when detecting small targets in the complex background; while its fast version has high computational efficiency. The proposed algorithm can be used in infrared searching and tracking systems.