Many scheduling algorithms have been studied to guarantee the time constraints of real-time processes. Scheduling decision of these algorithms is usually based on parameters which are assumed to be crisp. However, in many circumstances the values of these parameters are vague. The vagueness of parameters suggests that we make use of fuzzy logic to decide in what order the requests should be executed to better utilize the system and as a result reduce the chance of a request being missed. We have proposed a new fuzzy algorithm called highest fuzzy priority first. The performance of this algorithm is compared with the well-known earliest deadline first algorithm through simulation. For both algorithms, tasks are considered to be non-preemtable. Simulation results show that this fuzzy approach outperforms the earliest deadline first has algorithm in that it decreases the number of missed deadlines and serves more important tasks better.