Due to the passive nature of Intelligent Reflecting Surface (IRS), channel estimation is a fundamental challenge in IRS-aided wireless networks. Particularly, as the number of IRS reflecting elements and/or that of IRS-served users increase, the channel training overhead becomes excessively high. To tackle this challenge, we propose in this paper a new anchor-assisted two-phase channel estimation scheme, where two anchor nodes, namely A1 and A2, are deployed near the IRS for helping the base station (BS) to acquire the cascaded BS-IRS-user channels. Specifically, in the first phase, the partial channel state information (CSI), i.e., the element-wise channel gain square, of the BS-IRS link is obtained by estimating the BS-IRS-A1/A2 channels and the A1-IRS-A2 channel, separately. Then, in the second phase, by leveraging such partial knowledge of the BS-IRS channel that is common to all users, the individual cascaded BS-IRS-user channels are efficiently estimated. Simulation results demonstrate that the proposed anchor-assisted channel estimation scheme is able to achieve comparable mean-squared error (MSE) performance as compared to the conventional scheme, but with significantly reduced channel training time.