In the natural environment and engineering scenarios, there are not only bare unsaturated soils but also unsaturated soils covered by vegetation (i.e., unsaturated vegetated soils). For the unsaturated vegetated soil with a uniform root architecture, on the basis of considering the effects of roots on the hydrological properties, the linearized governing equations for one-dimensional transient seepage of water are acquired by some simplifying assumptions and variable substitution. The analytical solution for one-dimensional transient seepage of water in the unsaturated vegetated soil is obtained through the methods of separation of variable and series transformation. Subsequently, the computational results of this analytical solution have been compared with those of the existing analytical solution and the corresponding finite-difference solution to verify its reasonableness. Finally, a simple vegetated cover is taken as an example to analyze the influences of root-related parameters on its effectiveness in blocking rainwater infiltration. The results show that the cumulative leakage CQ_b at the bottom zone of a vegetated cover under the same rainfall scenario is smaller than that of a single cover without vegetation, and an increase in the rooted soil thickness l_g enhances the effectiveness of the vegetated cover in blocking rainwater leakage. The increase of the transpiration rate T_p significantly reduces the leakage rate at the bottom zone of the vegetated cover under the rainfall scenario, and the cumulative leakage CQ_b tends to decrease linearly with an increase in T_p. Compared with the extreme case where the root volume ratio R_v is zero and the effects of roots on the hydrological properties of soil are ignored, the effectiveness of the vegetated cover in blocking rainwater leakage is enhanced when the saturated permeability coefficient of the rooted soil decreases due to the value R_v, and conversely, it is weakened. Overall, this study could provide scientific guidance for engineering practices related to water infiltration in unsaturated vegetated soils.