Slow shot velocity and its acceleration phase in the shot sleeve have great influence on the flow pattern of the liquid metal in the shot sleeve. In this paper, a three-dimensional model based on the SOLA-VOF algorithm was developed and used to simulate the flow of melt in the shot sleeve. The mathematical model was verified by water analog experiments with constant plunger velocities. Based on numerical simulation results, the influences of the plunger acceleration on the wave profile of the liquid metal in the shot sleeve under different fill ratios and sleeve diameters were investigated. The results indicated that in order to avoid air entrapment in the shot sleeve, the optimal acceleration value to the critical slow shot velocity increases with the increase of the fill ratio, and the range of suitable acceleration becomes wider as well. With the same fill ratio, the value of suitable acceleration rises as the plunger diameter increases.