Background suppression is an important problem in infrared small target detection. The two-dimensional least mean square (TDLMS) filter is a widely used method, but its performance will decline when targets are embedded in a complex cluttered background. To fill the gap, variable step-size TDLMS, the neighborhood analysis technique, and the edge-directional TDLMS filter are developed but still cannot achieve a satisfying performance. Here, an adaptive method for background suppression is proposed. According to different characteristics of the pixels in homogeneous/target regions and inhomogeneous regions, two basic filters are first designed. Then a fuzzy edge estimation factor is introduced to combine them into a uniform framework, in which the two basic filters can be switched automatically to fit different kinds of pixels. Finally, a new mechanism to update and propagate the coefficients of the prediction window is constructed. It makes sure that the adaptive method works smoothly and reveals a potential to be implemented in parallel. The experimental results demonstrate that the proposed method achieves significant improvement in background suppression and detection performance.