Load demand scheduling of electricity consumers is an effective way to alleviate the peak power demand on the electricity grid and to combat the mismatch between generation and consumption. In this paper, we consider a scenario where multiple users cooperate to perform load demand scheduling in order to minimize the electricity generation cost. With the help of a central controller in the grid, a globally optimal solution can be achieved. However, this centralized solution may not always be feasible since it requires a huge amount of communication and the grid may not be equipped with such a central controller at all. Therefore, we propose a distributed load demand scheduling algorithm where each end user schedules its own tasks based on the partial information provided by other users. Simulation results show that this distributed load demand scheduling is able to achieve near-optimal solutions that has very little performance degradation compared to the centralized method.