The acceleration performance of the pellet injection system used in a superconducting linear acceleration to fuel the nuclear fusion reactor has been investigated numerically. To this end, the numerical model has been developed for analyzing the shielding current density in a high-temperature superconducting (HTS) film by using the finite element method. By using the code, the pellet injection system has been simulated. The results of the computations show that, for the single acceleration coil, the final velocity increases almost in proportion to the height of the coil. For the multiple coils, the pellet container can be accelerated to 5 km/s or more by about 6.87 seconds. Consequently, the length of the electromagnetic rails for a single coil becomes shorter than that for the multiple coils.