<p>The enhancement of the acceleration performance of a superconducting linear acceleration (SLA) system to inject the pellet container has been investigated numerically. To this end, a numerical code used in the finite element method has been developed for analyzing the shielding current density in a high-temperature superconducting film. In addition, the on/off method and the normalized Gaussian network (NGnet) method have been implemented in the code for the shape optimization of an acceleration coil, and the non-dominated sorting genetic algorithms-II have been used as the optimization method. The results of the computations show that the speed of the pellet container for the current profile of the optimized coil is significantly faster than that for the homogeneous current profile of the coil. However, for the on/off method, the current profile is scattered, whereas the coil shape becomes hollow for the NGnet method. Consequently, the NGnet method is an effective tool for improving the acceleration performance of the SLA system and for obtaining a coil shape that is easy to design.</p>