The diffraction grating is an important device that makes use of the diffraction of light to produce spectra. Diffraction is also fundamental in other applications such as x-ray diffraction studies of crystals and holography. We proposed a design of Bragg grating waveguide to investigate the behavior of diffraction of light at different incident angle and wavelengths. Using finite difference time domain (FDTD) photonics simulation software the performance of proposed waveguide is observed in term of output power, electric field, diffraction efficiency (DE) and signal to noise ratio (SNR). It is found that the proposed waveguide provides better diffracted light with electric field distribution with 1.969 v/m, Diffraction efficiency 8%, and SNR (25.5 dB) at 1.55µm wavelength and 00 degrees of incident angle