It is challenging to acquire accurate channel knowledge for sufficient beamforming gain because of the large number of antennas. In this paper, a deep learning aided channel estimation algorithm is proposed for mmWave cellular systems, in which both the base station (BS) and mobile station (MS) gain directional beamforming by employing large antenna arrays. We consider the off-grid (OG) mmWave channel estimation and propose a deep network architecture for solving this problem, which is different from most existing works concerning the compressed sensing (CS)-based channel estimation. Firstly, the off-grid channel model is used to relieve the basis mismatch issue by exploiting first-order Taylor-series approximation of the array manifold taken on a fixed grid of both BS and MS. Secondly, a new formulation of this off-grid channel estimation problem is solved by using a low computational complexity alternating direction method of multipliers (ADMM)-based algorithm, dubbed ADMM-OG algorithm. Thirdly, the idea of algorithm unrolling guides us to design a deep network architecture ADMM-OGChannelNet corresponding to the ADMM-OG algorithm for the mmWave channel estimation. Based on the interpretability of this deep network architecture, the optimal parameters of this network can be learned without tuning in a hand-crafted way. The Cramér-Rao bound (CRB) of the off-grid channel model is derived for performance comparison as well. Finally, from the simulation results, we can verify that the ADMM-OGChannelNet has better estimation accuracy and relatively low computational complexity compared with the state-of-the-art algorithms.