Protein structure alignment is one of the fundamental problems in computational structure biology. A variety of algorithms have been developed to address this important issue in the past decade. However, due to their heuristic nature, current structure alignment methods all more or less suffer from suboptimal alignment and/or over-fragmentation and may lead to a biologically wrong alignment. To overcome these limitations, we have developed an accurate topology-independent and global structure alignment method through an FFT-based exhaustive search algorithm, which is referred to as FTAlign.Our FTAlign algorithm was extensively tested on six commonly-used data sets and compared with seven state-of-the-art structure alignment approaches, TMalign, DeepAlign, Kpax, 3DCOMB, MICAN, SPalignNS, and CLICK. It was shown that FTAlign outperformed the other seven methods in reproducing manually-curated alignments and obtained a high success rate of 96.7% and 90.0% on two gold-standard benchmarks, MALIDUP and MALISAM, respectively. Moreover, FTAlign also achieved the overall best performance in terms of biologically meaningful structure overlap (SO) and TMscore on both the sequential alignment test sets including MALIDUP, MALISAM, and 64 difficult cases from HOMSTRAD, and the non-sequential sets including MALIDUP-NS, MALISAM-NS, 199 topology-different cases, where FTAlign especially showed more advantage for non-sequential alignment. Despite its global search feature, FTAlign is also computationally efficient and can normally complete a pairwise alignment within one second.http://huanglab.phys.hust.edu.cn/ftalign/.None.