The gas-assisted injection molding (GAIM) process is often adopted to compensate for shrinkage and improve part quality. However, gas penetrations consisting of primary and secondary penetrations will usually induce “fingering” behaviors, in which gas penetrates unevenly inside the parts and may lead to significant reductions in part stiffness. Due to the dynamic instability and complex material properties of fingering behaviors, it is desirable to be able to predict the behaviors with the help of simulation tools. In order to simulate the fingering behaviors, it is necessary to calculate the gas penetrations with a sharp interface between melt and gas, and to incorporate the compressibility of materials with high accuracy. In this study, we present a three-dimensional finite volume method that considers the non-Newtonian compressible flow with a high-resolution interface scheme for simulating the fingering behaviors during the GAIM process. A thin plate case is done to validate the accuracy and the capability of our proposed method to predict the sharp interface for primary and secondary gas penetrations. Then, we present a fish-bone plate with branches to investigate the gas penetrations on fingering behaviors through the dynamic simulation results and the specific volume changes on a pressure-volume-temperature diagram.