This work introduces local search based algorithms as a new technique for the Grid scheduling problem. Specific algorithms based on dispatching rules and local search were proposed and implemented to generate schedule for dynamically arriving jobs. Algorithm performance was compared with typical queue-based algorithms from the point of view of objective function optimisation and time required to generate scheduling solutions. Grid environment was simulated by Alea Simulator which is based on modified and extended Grid- Sim toolkit. The results showed that local search based algorithms may be promising technique with better performance than queue-based approaches while still fast enough to provide solution in a reasonable time.