In this paper, we study efficient channel estimation design for an extremely large-scale intelligent reflecting surface (XL-IRS) assisted multi-user communication systems, where both the base station (BS) and users are located in the near-field region of the XL-IRS. Two unique channel characteristics of XL-IRS are considered, namely, the near-field spherical wavefronts and double-sided visibility regions (VRs) at the BS and users, which render the channel estimation for XL-IRS highly challenging. To address this issue, we propose in this paper an efficient three-step XL-IRS channel estimation method. Specifically, in the first step, an anchor node is delicately deployed near the XL-IRS to estimate the cascaded BS-IRS-anchor channel. Then, an efficient VR detection method is devised to estimate the VR information between the BS and XL-IRS. In this way, only the channels from the visible XL-IRS elements to the BS are estimated, thereby reducing the dimension of the cascaded BS-IRS-users channels to be estimated. Third, by leveraging the common BS-IRS channel, the cascaded channels for all users are consecutively estimated accounting for the VRs of the IRS-user channels. Finally, numerical results are provided to demonstrate the effectiveness of our proposed channel estimation scheme as compared to various benchmark schemes.