In recent years, the achievement of the electromagnetically induced transparency (EIT) effect based on the guided-mode resonance (GMR) effect has attracted extensive attention. However, few works have achieved a double EIT-like effect using this method. In this paper, we numerically achieve a double EIT-like effect in a GMR system with a three-layer silicon nitride waveguide grating structure (WGS), using the multi-level atomic system model for theoretical explanation. In terms of slow light performance, the corresponding two delay times reach 22.59 ps and 8.43 ps, respectively. We also investigate the influence of wavelength detuning of different GMR modes on the transparent window and slow light performance. Furthermore, a wide-band flat-top transparent window was also achieved by appropriately adjusting the wavelength detuning between GMR modes. These results indicate that the EIT-like effect in the WGS has potential application prospects in low-loss slow optical devices, optical sensing, and optical communications.