Modeling and simulating a power distribution network (PDN) for printed circuit boards with irregular board shapes and multi-layer stackup is computationally inefficient using full-wave simulations. This paper presents a new concept of using deep learning for PDN impedance prediction. A boundary element method (BEM) is applied to efficiently calculate the impedance for arbitrary board shape and stackup. Then over one million boards with different shapes, stackup, integrated circuits (IC) location, and decap placement are randomly generated to train a deep neural network (DNN). The trained DNN can predict the impedance accurately for new board configurations that have not been used for training. The consumed time using the trained DNN is only 0.1 s, which is over 100 times faster than the BEM method and 10 000 times faster than full-wave simulations.