Based on our previous work, an algorithm called AWS is proposed in this paper for a double-layer workflow scheduling approach for the Grid. AWS aims to overcome difficulties brought about by the clustered resource distribution within the Grid. It partitions a workflow graph according to features of available resource clusters and of the graph itself. It does not require detailed status information or control privilege on every Grid resource for Grid schedulers at the global Grid level. As a result, the dependence on Grid information services is reduced and, at the same time, the higher priority of local resource management policies is respected. Experimental results show that AWS is adaptive to the Grid circumstances and its performance approaches ideal global fine-granularity scheduling methods.