It has been proved that there is no optimal online scheduler for uniform parallel machines. Despite its non-optimality, EDF is an appropriate algorithm to use in such environments. However, its performance significantly degrades in overloaded situations. Moreover, EDF produces a relatively large number of migrations which may prove unacceptable for use on some parallel machines. In this paper a new deadline- based algorithm for scheduling real-time tasks on uniform parallel machines is presented. The performance of this algorithm is then compared with that of EDF algorithm. It is shown that our proposed approach not only demonstrates a performance close to that of EDF in non-overloaded conditions but also has supremacy over EDF in overloaded situations in many aspects. Furthermore, it imposes much less overhead on the system.