Grid computing is a solution in fulfilling the needs of high performance computing which has a main idea of joining the heterogeneous, distributed resources to form a single, integrated system. This technology has been developed rapidly and become one of interesting research topic for the computer scientists. This research will try to design and simulate an e-learning computer network that utilize Grid computing technology (or just mentioned as Grid). This computer network will be called Indonesian Education Grid or abbreviated as IndoEdu-Grid. Grid is used because it has some advantages, such as supports the use of heterogeneous resources (hardware or software), distributed well without existence of monopolies, not expensive, and able to maximize the utilizing of the provided resources. The establishment of the network without equipping it with Grid computing ability will cause redundancies such as the idle resources, especially resources with a little number of accesses. This brings us to the thought to establish IndoEdu-Grid. IndoEdu-Grid has to be established using the effective network topology so the users are able to effectively utilize the network. It is important to do a simulation to find the most effective network topology. The input of the simulation will be some configurations of network topology and the output will be the conclusion about the most appropriate network topology. The simulation is built using GridSim toolkit, a Java-based toolkit. The simulation will handle three conditions or scenarios which have different network topologies based on their routers and links configuration. Each scenario will be run in the simulator using two packet scheduling algorithm, that are FIFO (First In First Out) Scheduler and SCFQ (Self-Clocked Fair Queuing) Scheduler. The processing time of the job‟s packets will be evaluated to determine the most effective network topology for IndoEdu-Grid. The simulation result showed that if FIFO scheduling algorithm is used, then the most appropriate network topology is the topology that has the lowest number of hops for its packets, which is the third scenario that only has leaf routers and if SCFQ scheduling algorithm is used, then the most appropriate network topology is the topology that allows its packets with the same priorities have less possibility to meet each other in one router or link, which is the first scenario that has leaf routers, edge routers, and core routers that configured hierarchically. The simulation result also showed that SCFQ scheduling algorithm can decrease the packets lifetime at router that has very crowded traffics. This fact implies to the decrease of the whole job processing time. Thus, the simulation gives conclusion that it is better if the first scenario with SCFQ scheduling algorithm is used.