We theoretically and numerically investigate the influence of high-order effects on a trapped soliton pumped by a high-power pulse during nonlinear propagation. According to the moment method, some evolution rules of a trapped soliton are found in the presence of high-order effects by theoretically analyzing five moment parameters. Further, the temporal and spectral evolutions of a trapped soliton are numerically studied in details. It is demonstrated that the third-order dispersion (TOD) only affects the center position of a trapped soliton, b...