We present the first group of GHz broadband SH0 mode acoustic delay lines (ADLs). The implemented ADLs adopt unidirectional transducer designs in a suspended X-cut lithium niobate thin film. The design space of the SH0 mode ADLs at GHz is first theoretically investigated, showing that the large coupling and sufficient spectral clearance to adjacent modes collectively enable the broadband performance of SH0 delay lines. The fabricated devices show 3-dB fractional bandwidth ranging from 4% to 34.3% insertion loss between 3.4 and 11.3 dB. Multiple delay lines have been demonstrated with center frequencies from 0.7 to 1.2 GHz, showing great frequency scalability. The propagation characteristics of SH0 in lithium niobate thin film are experimentally extracted. The demonstrated ADLs can potentially facilitate broadband signal processing applications.