Service level agreements (SLAs) are currently one of the major research topics in grid computing. Among many system components for supporting of SLA-aware Grid jobs, the SLA mapping module holds an important position and the capability of the mapping module depends on the runtime of the mapping algorithm. With the previously proposed mapping algorithm, the mapping module may develop into the bottleneck of the system if many requests come in during a short period of time. This paper presents a parallel mapping algorithm to map heavy communication SLA-based workflow onto Grid resources which can cope with the problem. Performance measurements thereby deliver evaluation results showing the quality of the method.