Massive multiple-input multiple-output (MIMO) with lens antenna array, referred to as beamspace MIMO, is attractive for millimeter wave (mmWave) communications, since it can realize the adequate beamforming gain with a small number of radio frequency (RF) chains. This paper addresses wideband channel estimation for mmWave beamspace MIMO. Specifically, a two-stage channel estimation scheme is proposed. In the first stage, we utilize multi-task sparse Bayesian learning (MT-SBL) to coarsely estimate the beamspace channel vectors, each corresponding to one OFDM subcarrier. In the second stage, we re-formulate the channel estimation problem by artfully exploiting the characteristics of beamspace channels. Then we develop an expectation maximization (EM) based algorithm to estimate the parameters involved in the formulation, thereby refining the channel estimates. Compared with the state-of-the-art counterparts, the proposed scheme can achieve much better performance while requiring a lower training overhead.