A single mode waveguide grating coupler based on multiple Si-SiO₂ pairs onto Si substrate has been designed. Numerical analysis has been carried out to calculate optimum thickness of the layers of Si-SiO₂ that ensures the constructive interference between reflected waves and actual guided wave for high coupling efficiency. Based on the results, an optimal design is developed and modeled by using a 2-D finite difference time domain (2-D FDTD) simulator that dictates a coupling efficiency of as much as 78% (-1.07 dB) at the wavelength of 1550 nm, and a 1-dB bandwidth of 77 nm. The numerical method will be useful to calculate the optimum thicknesses of the layers for any reflector based grating coupler of different materials.