This study presents the design and simulation of a fuzzy control algorithm for managing the traffic of two or more elevators in high-rise buildings. The fuzzy elevator group control system (FEGCS) introduced herein is designed to respond to a new hall call by determining the most suitable car based on an evaluation function computed for each car. The car with the lowest value of evaluation function is selected to serve the hall call. The evaluation function is computed by summation of two terms. The first term is the estimated arrival time to the floor where the hall call occurs. The second term consists of the floor priority coefficient multiplied by a fuzzy control variable resulted from Mamdani type fuzzy inference, controlling the effectiveness of floor priority. To increase the performance of the elevator group three major linguistic variables are introduced within a set of fuzzy rules. These include the average waiting time (AWT), power consumption (PC), and floor traffic (FT). During the hours of low passenger traffic, high fuzzy control values resulted in the cars to be positioned at the floors to which high priority values are assigned. When the passenger traffic is high, the low fuzzy control values reduce the importance of priority of floors, rather the estimated arrival time is to be minimized.