When capillary flow occurs in a uniform porous medium, the depth of penetration is known to increase as the square root of time. However, we demonstrate in this study that the depth of penetration in multi-section porous layers with variation in width and height against the flow time is modified from this diffusive-like response, and liquids can pass through porous systems more readily in one direction than the other. We show here in a model and an experiment that the flow time for a negative gradient of cross-sectional widths is smaller than that for a positive gradient at the given total height of porous layers. The effect of width and height of local layers on capillary flow is quantitatively analyzed, and optimal parameters are obtained to facilitate the fastest flow.