The hybrid sleep mode of optical network unit was introduced into ethernet passive optical network for multicast traffic, and the energy saving algorithm for multicast traffic and improved energy saving algorithm for multicast traffic were proposed. The two algorithms sleep the idle components of optical network units and reduce the wakeup times of optical network units by constraints, so that the energy consumption of optical network units can be reduced. Compared with energy saving algorithms for multicast traffic, the improved energy saving algorithms for multicast traffic adds a constraint for optical network units wakeup, so reduces the wakeup times of optical network units further. Simulation results show that, the two proposed algorithms save more energy than the previous algorithm with guaranteed packet delay. Moreover, the improved energy saving algorithms for multicast traffic saves more energy than energy saving algorithms for multicast traffic, which shows that the adding constraint contributes to the reduction of the wakeup times and the energy consumption of optical network units.