Disclosed are an IPv4/IPv6 dual stack software/hardware apparatus for processing an Internet packet and a method thereof. The IPv4/IPv6 dual stack software/hardware apparatus for processing an internet packet includes: a hardware type packet processor configured to process the Internet packet by a system logic circuit; a software type packet processor configured to process the Internet packet according to execution of a previously prepared program; and a packet process controller configured to receive the Internet packet to control the hardware type packet processor to process the Internet packet of a preset protocol, and to control the software type packet processor to process the Internet packet of another preset protocol.