Spontaneous imbibition flows within confined geometries are commonly encountered in both natural phenomena and industrial applications. A profound knowledge of the underlying flow dynamics benefits a broad spectrum of engineering practices. Nonetheless, within this area, especially concerning complex geometries, there exists a substantial research gap. This work centers on the cylinder-plane geometry, employing a combined theoretical and numerical approach to investigate the process of a wetting film wrapping a cylinder corner. It is found that the advance of the liquid front generally follows the Lucas-Washburn kinetics, i.e., $\thalf$ scaling, but it also depends on the dynamics of the liquid source. Furthermore, we provide a theoretical estimation of the timescale associated with the imbibition process. Notably, this timescale is highly dependent on the wettability condition and the properties of the involved liquid. Importantly, the practicability of our theoretical framework is well confirmed by the numerical experiments.