This paper studies the online scheduling on unrelated parallel machines with machine eligibility constraints. The jobs arrive over time and the maximum completion time is the optimization objective. To our best knowledge, the considered problem is never been studied before. Firstly an mathematical model is established. Then, both a heuristic algorithm and a meta-heuristic algorithm are proposed to obtain approximate optimal solutions. The two online algorithms are based on greedy algorithm and machine preference. Finally, the performances of the two proposed online algorithms are compared with an online algorithm based on ERT through extensive experiments, which show that both the two algorithms have effective performances.