In Hybrid networks, which synergistically mix together wired and wireless links to achieve flexible and reliable communication, it is particularly challenging to routing selfish tasks since each task wish to finish transmission as early as possible and its decision could have impacts on the others. In this paper, we investigate the problem to route a given set of selfish tasks in hybrid networks. Under a unified cost model, the competitive behaviors of selfish players are modeled as a noncooperative game. We show the game is ordinal potential, and the existence of a pure-Nash Equilibrium (pure-NE) is therefore guaranteed. We also design a routing scheme, called Selfish Task-Driven Routing (STaR), to achieve a pure-NE. Extensive simulations show that our scheme can not only efficiently converge to an equilibrium but also outperform other source routing protocols regarding the completion time and load balancing.