Demand response (DR) is an important characteristic of a smart grid that benefits both power system operators and electricity consumers. In this paper, an optimal DR with a dynamic electricity price limit is proposed for a grid-connected ac/dc hybrid microgrid. The considered system consists of ac/dc loads, photovoltaic source, and battery energy storage system. The electricity price limit is determined using day-ahead pricing of electricity, predictions of ac/dc load, and PV power profiles. An optimal rule-based DR control algorithm that determines day-ahead charge/discharge schedules of battery for minimizing the energy costs of the system is developed. The rules are formulated such that there is no power drawn from the grid when the electricity price is more than the electricity price limit while ensuring that the state of charge (SoC) of battery at the end of the day is same as SoC of the start of the day. The optimal inputs required for applying proposed DR are determined using genetic algorithm in MATLAB.