We present an interface tracking algorithm that incorporates essential pore-scale invasion mechanisms for simulating multiphase flow in porous media in capillary dominated regime. The algorithm allows the capture of the actual shape of porous medium with complex geometrical features, including both convex and concave particles or irregular channels. It also incorporates the sharp edge pinning effect such that pinning of menisci at corners can be naturally taken into account. We firstly conduct simulations under imbibition and drainage conditions in a single junction micromodel and in disordered porous media for validation. It is shown that the invasion mechanisms at pore scale are accurately captured, and the macroscopic invasion morphology in porous media are reproduced. A series of simulations for fluid displacement processes are carried out across a wide range of intrinsic contact angles in a two-dimensional representation of a Berea sandstone. The transition between stable displacement and capillary fingering is characterized using displacement efficiency, fractal dimension, and fluid-fluid interfacial length. This work deepens the understanding of fluid-fluid displacement processes in porous media. Furthermore, the presented interface tracking algorithm offers a highly efficient tool for further exploration of effects of wettability, geometry, and topology on multiphase flow in realistic porous materials.