Application mapping algorithm for reconfigurable architecture is one of the major research direction in reconfigurable computing. In this paper, we analyze the data memory bank conflict problem of the ACRPs (Application Customized Reconfigurable Pipelines) when exploiting the data parallelism and a conflict-free iteration-data mapping algorithm based on the operation mapping results is proposed to conquer the bank conflict problem. The experiments showed that ACRP can exploit the CFU-, pipeline-and data-level parallelism efficiently. More specifically, the iteration-data mapping algorithm avoids the bank conflicts while exploiting the data parallelism to increase the throughput.