We consider the problem of channel estimation in hybrid transceiver architectures operating in millimeter wave (mmWave) band. Due to the dynamic features of the environment and the sensitivity of mmWave bands to blockage and deafness, it is important to estimate mmWave channels with a low complexity and high performance algorithm. In this regard, we exploit the sparse structure of the frequency-selective mmWave channels and formulate the channel estimation problem as a sparse signal reconstruction in frequency domain. In order to solve the estimation problem, we propose a multi-stage based low complexity algorithm. Simulation results show that the proposed algorithm significantly reduces the computational complexity while preserving the quality of the estimation.