Abstract: In this talk, we will first recall some preliminaries about the Chern-Ricci flow, then we talk about the properties of the Chern-Ricci flow on the Inoue surfaces which are non-Kahler compact complex surfaces of type Class VII. We prove that, after an initial conformal change, the flow always collapses the Inoue surface to a circle at infinite time, in the sense of Gromov-Hausdorff. This is a joint work with Professor Shouwen Fang, Valentino Tosatti and Ben Weinkove.