Intelligent reflecting surface (IRS) has emerged as a promising paradigm to improve the capacity and reliability of a wireless communication system by smartly reconfiguring the wireless propagation environment. To achieve the promising gains of IRS, the acquisition of the channel state information (CSI) is essential, which however is practically difficult since the IRS does not employ any transmit/receive radio frequency (RF) chains in general and it has limited signal processing capability. In this paper, we study the uplink channel estimation problem for an IRS-aided multiuser single-input multi-output (SIMO) system, and propose a novel two-phase channel estimation (2PCE) strategy which can alleviate the negative effects caused by error propagation in the existing three-phase channel estimation approach, i.e., the channel estimation errors in previous phases will deteriorate the estimation performance in later phases, and enhance the channel estimation performance with the same amount of channel training overhead as in the existing approach. Moreover, the asymptotic mean squared error (MSE) of the 2PCE strategy is analyzed when the least-square (LS) channel estimation method is employed, and we show that the 2PCE strategy can outperform the existing approach. Finally, extensive simulation results are presented to validate the effectiveness of the 2PCE strategy.