A tunneling-based mobility support method and apparatus is provided which supports a mobility of a mobile node in a heterogeneous network regardless of IP versions (IPv4/IPv6). The mobility support apparatus includes a load balancer, a plurality of mobility support servers, and a plurality of end routers each being TCP connected to each of the mobility support servers. When receiving a tunnel establishment request message from the mobile node, the load balancer selects one mobility supports server from a plurality of mobility support servers to control a mobility service for the mobile node. The selected mobility support server selects a plurality of tunnel end addresses of one end router from the plurality of end routers to establish an IP tunnel with the mobile node according to a predetermined criterion, forwards the tunnel establishment request message to the end router, and sends the mobile node a tunnel establishment response message including the tunnel end address of the selected end router.