Unexpectedly fast flow (up to 1 m/s) of water in graphene nanoslits was reported in experiments, revealing the breakdown of Washburn's equation with no-slip condition. In this work, the imbibition dynamics of water into graphene nanoslits, ranging in width from one to ten atomic planes, is explored via Molecular Dynamics. The density of imbibed water in the nanoslit is analyzed and it depends on the channel width. Moreover, the interfacial tensions, equilibrium contact angle of water on the graphene sheet, and slip lengths of steady flow in nanoslits are evaluated. The slip length is found to decrease with increasing the channel width. The analyses of spontaneous capillary flow indicate that the time evolution of the penetration length follows Washburn's equation qualitatively and the flow rates are comparable to the experimental results. However, the dependence of the imbibition rate on the channel width does not agree with Washburn's equation at all. As the channel width-dependent slip length is introduced, the imbibition dynamics can be reasonably described by Washburn's equation. The channel width-dependent behavior can be explained by the variation of the water state with the channel width, which can be realized by the changes of water densities and hydrogen bonds with the channel width.