Abstract: We usually assume that reflection data only consist of primary during seismic data processing. And surface-related multiple in seismic prospecting data is usually suppressed as coherent noise. Data-driven feedback iteration approach based on wave equation prediction is an effective method which can suppress surface-related multiple from complex earth media. This algorithm can be performed by either series expansion or iteration. In this paper, the two implementation approaches for feedback iteration based on wave equation prediction is researched from theory description and applied effect analysis perspective, this paper also give specific explanation on basic principles of the two approaches. In this paper, surface-related multiple is predicted by collaborative parallel calculation of GPU/CPU, which can improve the situation of low calculation efficiency by CPU. With the development of GPU accelerating technology, computation efficiency for seismic data processing is improved. This will be helpful when applying iteration approach on suppressing surface-related multiple of large scale seismic data. The shot data with surface-related multiple and SMAART model with surface-related multiple from complex media have been tested in the paper. In this research, result of series expansion approach shows it needs to be obtained by summing many prediction items, and in fact the number of predictable items is usually limited, this will lead to errors in the multiple suppression process. In contrast to series expansion approach, we can obtain better multiple suppression effect by iteration approach. The effect is usually ideal when iteration approach is used after three times. Iteration can also be combined with many other approaches, it shows more flexibility. Different amount of adaptive matching subtraction are required for iteration and series expansion approach, so the computation cost of iteration is slightly higher than that of series expansion approach, but GPU accelerating method can solve the problem in some degree. Iteration approach is more effective on complex media, so that it has more widely applied range and development prospect.