We consider the imbibition of a liquid droplet of finite size on a rough surface and theoretically show that the imbibition dynamics is significantly slower than. the familiar Washburn diffusive dynamics, similar to t(0.5). The imbibition does not follow a simple os power law. The droplet starts to imbibe with similar to t(0.5) dynamics but progressively becomes slower with time. The slower imbibition is mainly attributed to the finite size of the droplet, resulting in a limited capillary driving force as compared to a steady capillary driving force in the case of imbibition from a steady source.