A real-time electricity management strategy is studied for the prosumers without energy storage device, which have dual role of power supplier and consumer in smart grid. Firstly, a real-time power management model with the constraint of maximum tolerance of power demand is constructed. Based on Lyapunov optimization theory, a real-time electricity management algorithm is proposed to maximize the power user’s revenue generated by selling electricity to external grid while guaranteeing the service delay of electricity demand within given tolerable period, considering time-varying price of power system, uncertainty of user generation and flexible load to control and manage the power consumption of the prosumer and the electricity trading with the grid. The proposed algorithm has low complexity and does not need to know the statistical characteristics of power demand, electricity price and renewable energy power generation. Theoretical analysis shows that the proposed algorithm can make the optimization target infinitely close to optimum, with guarantee of the delay of electricity demand in tolerance range. Finally, simulation results are given to show that the proposed algorithm outperforms the existing algorithms and several other greedy algorithms, and the impact of the different parameters on the performance of algorithm is analyzed, which provides a theoretical basis of power management of prosumer and helps the stable operation of power grid.