This paper deals with a scheduling problem in a flexible job shop with multi-level job structures where end products are assembled from sub-assemblies or manufactured components. For such shops MRP (Material Requirement Planning) logic is frequently used to synchronize and pace the production activities for the required parts. However, in MRP, the planning of operational-level activities is left to short term scheduling. So, we need a good scheduling algorithm to generate feasible schedules taking into account shop floor characteristics and multi-level job structures used in MRP. In this paper, we present a GA (Genetic Algorithm) solution for this complex scheduling problem based on a new gene to reflect the machine assignment, operation sequences and the levels of the operations relative to final assembly operation. The relative operation level is the control parameter that paces the completion timing of the components belonging to the same branch in the multi-level job hierarchy. We compare the genetic algorithm with several dispatching rules in terms of total tardiness and the genetic algorithm shows outstanding performance for about forty modified standard job-shop problem instances.