By employing the lens antenna array, beamspace MIMO can utilize beam selection to reduce the number of required RF chains in mmWave massive MIMO systems without obvious performance loss. However, to achieve the capacityapproaching performance, beam selection requires the accurate information of beamspace channel of large size, which is challenging, especially when the number of RF chains is limited. To solve this problem, in this paper we propose a reliable support detection (SD)-based channel estimation scheme. Specifically, we propose to decompose the total beamspace channel estimation problem into a series of sub-problems, each of which only considers one sparse channel component. For each channel component, we first reliably detect its support by utilizing the structural characteristics of mmWave beamspace channel. Then, the influence of this channel component is removed from the total beamspace channel estimation problem. After the supports of all channel components have been detected, the nonzero elements of the sparse beamspace channel can be estimated with low pilot overhead. Simulation results show that the proposed SD-based channel estimation outperforms conventional schemes and enjoys satisfying accuracy, even in the low SNR region.