A system for multicasting multimedia contents using Multicast Listener Discovery protocols according IPv6 standards and a method of reproducing multimedia contents using the same. The method of reproducing multimedia contents includes transmitting a first packet including channel information regarding a channel selected by a user, receiving a second packet including multimedia contents transmitted by multicasting through the selected channel in response to the first packet, and reproducing the multimedia contents included in the received second packet. Multicast packets transmitted to a router in a connection network by multicasting can be transmitted to home multimedia devices, so that congestion of the Internet in the IPv6 environment by an increased amount of data can be prevented.