Phase field method has been widely utilized to study multiphase flow problems, but has seldom been applied to the study of imbibition. Previous methods used to simulate imbibition, such as moving mesh method, need to specify capillary pressure as a boundary condition a priori, whereas phase field method can calculate capillary pressure automatically for various geometries. Therefore, phase field method would be a versatile tool for the study of imbibition in various geometries. In this paper, phase field method is employed to solve dynamical imbibition problem in various geometries, including straight tube, conical tube and structures in which the topology changes. The variation of the imbibition height with respect to time from phase field simulation is verified with theoretical predictions from Lucas-Washburn law in a straight capillary tube with three gravitational scenarios. In addition, the capillary pressure and velocity field are found to be consistent with Laplace-Young equation and Hagen-Poiseuille equation in various geometries. The applicability and accuracy of the phase field method for the study of imbibition in structures with changing topology are also discussed.