The hybrid multiple-input-multiple-output (MIMO) transceiver architecture is a promising solution to reducing hardware and power cost at millimeter-wave (mmWave) frequencies. However, channel estimation is a major issue for the deployment such system models. Thus, this work shows that by exploiting the sparse scattering nature of the mmWave channel, an efficent channel estimation algorithm can be achieved by utilizing state-of-the-art compressive sensing (CS) techniques. In general previous CS-based channel estimation methods consider an on-grid sparse signal representation problem, however this is not truly realistic to the scenario of mmWave massive MIMO systems. To achieve a more realistic channel estimation algorithm for the mmWave MIMO system, this work considers an off-grid signal model approach, i.e., the directions of sparse channels are not confined on the angular grid for sparse signal formulation. A new adaptive channel estimation method is proposed by using Bayesian CS (BCS) to accurately and efficiently sense channels in terms of an off-grid signal model. A measurement of recovery uncertainty output by BCS is exploited to adaptively design the sensing matrix, thereby improving its estimation performance.