IP (Internet Protocol) over WDM networks where IP packets are directly carried on the WDM network is expected to offer an infrastructure for the next generation Internet. For IP over WDM networks, a WDM protection mechanism is expected to provide a highly reliable network (i.e., robustness against the link/node failures). However, conventional IP also provides a reliability mechanism by its routing function. We thus need to treat functional partitioning or functional integration for IP over WDM networks with high reliability. In this paper, we first formulate an optimization problem for designing IP over WDM networks with protection functionalities of WDM networks, by which we can obtain IP over WDM networks with high reliability. Our formulation results in a mixed integer linear problem (MILP). However, it is known that MILP can be solved only for a small number of variables, in our case, nodes and/or wavelengths. We therefore propose two heuristic algorithms, min-hop-first and largest-traffic-first approaches in order to assign the wavelength for backup lightpath. Our results show that the min- hop-first approach takes fewer wavelengths to construct the reliable network, that is, all of lightpaths can be protected using the WDM protection mechanism. However, our largest-traffic- first approach is also a good choice in the sense that the approach can be saved the traffic volume increased at the IP router by the link failure.