A device and method for allocating the same Internet protocol (IP) address to all information terminals or hosts connected to a specific local network, which allows the hosts in the local network to gain access to the Internet while the hosts share a single IP address. The device includes a dynamic host configuration protocol (DHCP) client, a local access point, and a DHCP server spoofer. The DHCP client is allocated an IP address through a DHCP message communication with an Internet service provider. The Internet service provider includes a DHCP server for allocating IP addresses to the hosts and an Internet access gateway. The local access point includes a hardware address port translation (HAPT) module and a local IP address translation (LIAT) module. The HAPT module modifies a source medium access control (MAC) address and port number of a frame received from each host, stores the modified result in a HAPT table, and recovers a destination MAC address and port number of a frame received from the Internet service provider, referring to the HAPT table. The LIAT module prevents a collision occurring because the hosts have the same public IP address. The DHCP server spoofer implements a DHCP server function to allocate an IP address to each host.