We propose a new stratified waveguide grating coupler (SWGC) to couple light from a fiber at normal incidence into a planar waveguide. SWGCs are designed to operate in the strong coupling regime without intermediate optics between the fiber and the waveguide. Two-dimensional finite-difference time-domain simulation in conjunction with microgenetic algorithm optimization shows that about 72% coupling efficiency is possible for fiber (core size of 8.3 μm and ∆=0.36%) to slab waveguide (1.2- μm core and ∆=3.1%) coupling. We show that the phase-matching and Bragg conditions are simultaneously satisfied through the fundamental leaky mode.