To address how the spatial configuration of habitat fragmentation influences the persistence and the rate of spread of an invasive species, we consider three simple periodically fragmented environments, a lattice-like corridor environment, an island-like environment and a striped environment. By numerically analyzing Fisher's equation with a spatially varying diffusion coefficient and the intrinsic growth rate, we find the following. (1) When the scale of fragmentation is sufficiently large, the minimum favorable area needed for successful invasion reduces in the following order: lattice-like corridor, striped and island-like environments. (2) When the scale of fragmentation and the fraction of favorable area are sufficiently large, the spreading speeds along contiguous favorable habitats in the lattice-like corridor and striped environments are faster than the speeds across isolated favorable habitats in the island-like environment and the striped environment. (3) When the periodicity of fragmentation is relaxed by stochastically shifting the boundaries between favorable and unfavorable habitats, the average speed increases with increases in the irregularity of fragmentation.