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Millions of species are currently being sequenced and their genomes are being compared. Many of them have more complex genomes than model systems and raised novel challenges for genome alignment. Widely used local alignment strategies often produce limited or incongruous results when applied to genomes with dispersed repeats, long indels, and highly diverse sequences. Moreover, alignment using many-to-many or reciprocal best hit approaches conflicts with well-studied patterns between species with different rounds of whole-genome duplication or polyploidy levels. Here we introduce AnchorWave, which performs whole-genome duplication informed collinear anchor identification between genomes and performs base-pair resolution global alignments for collinear blocks using the wavefront algorithm and a 2-piece affine gap cost strategy. This strategy enables AnchorWave to precisely identify multi-kilobase indels generated by transposable element (TE) presence/absence variants (PAVs). When aligning two maize genomes, AnchorWave successfully recalled 87% of previously reported TE PAVs between two maize lines. By contrast, other genome alignment tools showed almost zero power for TE PAV recall. AnchorWave precisely aligns up to three times more of the genome than the closest competitive approach, when comparing diverse genomes. Moreover, AnchorWave recalls transcription factor binding sites (TFBSs) at a rate of 1.05-74.85 fold higher than other tools, while with significantly lower false positive alignments. AnchorWave shows obvious improvement when applied to genomes with dispersed repeats, active transposable elements, high sequence diversity and whole-genome duplication variation.