This paper puts forward a parallel abstract machine-parallel LE machine for transputer networks, which is based on the parallel LE semantic model. To increase the granularity of parallel process during the running time, the thread lazy process creation method is adapted in the LE machine, which decreases the time of process creation and explored the parallelism of the parallel process system at the same time. With the aid of bidirection linked stack frame structure, the prototype system of this method shows a good performance.