The Goos-Hänchen (GH) shift of light beam incident on graphene ribbon array is investigated by Green's function method. Due to the resonance effects of leaky surface plasmons on ribbons, the zeroth-order reflection field shows both giant positive and negative GH shifts. By tuning the graphene Fermi level, we can control the shift conveniently. This effect is important to graphene-based metasurface and electro-optical devices.