Recurrent U-Net (RU-Net) is employed for fast prediction of dynamic IR-drop when power distribution network (PDN) contains capacitor components. Each capacitor can be modeled by a resistor and a current source, which is a function of v(t-Δt) node voltages at time t - Δt allow the PDN to be solved at time t which then allows the analysis at t + Δt and so on. Provided that a quick prediction of IR-drop at one time instance can be done by U-Net, a image segmentation model, the analysis of PDN containing capacitors can be done by a number of U-Net instances connected in series, which become RU-Net architecture. Four input maps (effective PDN resistance map, PDN capacitance map, current map, and power pad distance map) are extracted from each layout clip, and are provided to RU-Net for IR-drop prediction. Experiments demonstrate that the proposed IR-drop prediction using the RU-Net is faster than a commercial tool by 16 times with about 12% error, while a simple U-Net-based prediction yields 19% error due to its inability to consider capacitors.