In this paper, we present a Double-Anchoring Based Tone Mapping (DABTM) algorithm for displaying high dynamic range (HDR) images. First, two anchoring values are obtained using the double-anchoring theory. Second, we use the two values to formulate the compressing operator, which can achieve the aim of tone mapping directly. A new method based on accelerated K-means for the decomposition of HDR images into groups (frameworks) is proposed. Most importantly, a group of piecewise-overlap linear functions is put forward to define the belongingness of pixels to their locating frameworks. Experiments show that our algorithm is capable of achieving dynamic range compression, while preserving fine details and avoiding common artifacts such as gradient reversals, halos, or loss of local contrast.