This paper presents DeepIA, a deep learning solution for faster and more accurate initial access (IA) in 5G millimeter wave (mmWave) networks when compared to conventional IA. By utilizing a subset of beams in the IA process, DeepIA removes the need for an exhaustive beam search thereby reducing the beam sweep time in IA. A deep neural network (DNN) is trained to learn the complex mapping from the received signal strengths (RSSs) collected with a reduced number of beams to the optimal spatial beam of the receiver (among a larger set of beams). In test time, DeepIA measures RSSs only from a small number of beams and runs the DNN to predict the best beam for IA. We show that DeepIA reduces the IA time by sweeping fewer beams and significantly outperforms the conventional IA's beam prediction accuracy in both line of sight (LoS) and non-line of sight (NLoS) mmWave channel conditions.