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Flat band slow light with high coupling efficiency is achieved in a simple one-dimensional grating waveguide. An ideal flat band indicating slow light with group index of 18.3 and bandwidth of 10.3 nm is obtained by plane wave expansion calculation. This result is also verified by inputting a Gaussian pulse into a 48.7-μm -long waveguide in a finite-difference time-domain simulation, in which optical pulse delay of 2.85 ps and group index of 17.54 can be observed. Meanwhile, by introducing a step taper, the coupling efficiency could be improved remarkably from below 20% for butt coupling to 70%. The proposed structure is an ideal candidate for wideband and compact low loss slow light delay lines or optical buffers in on-chip signal processing.