Accurate estimation of channel state information (CSI) is crucial to realize the full potential of massive multiple-input multiple-output (MIMO) communication systems. Despite the high accuracy of existing CSI estimators, the high computational complexity makes them impractical for real-world massive MIMO systems. So, developing a highly accurate and low-complexity estimator has been a long-standing challenge in the field of massive MIMO. In this paper, we present a channel estimation scheme that significantly reduces computational complexity while achieving high accuracy. Firstly, we design a two-stage training protocol whereby only part of the transmit and receive antennas are activated for signal emission or reception. Secondly, we apply the low-complexity Least-Square (LS) estimator to acquire two sub-blocks of the channel matrix. Relying on the inherent low-rank property of channel matrix, the complete channel matrix is reconstructed via a randomized matrix approximation technique. Thirdly, we consider three different power allocation schemes to further optimize the pilot power in 2-stage training process. The theoretical bounds of estimation error for our CSI estimator are derived, and the optimal power allocation strategy is thus obtained by minimizing this error bound. Numerical simulations are provided to demonstrate our proposed method. As shown, the theoretical error bound is tight, and the optimal power allocation can achieve the substantial gain. Our CSI estimator incurs the same complexity as the popular LS estimator, whilst the estimation accuracy is improved by ~5 dB, which has the great promise to new-generation massive MIMO communications.