Semi-Markov Decision Process (SMDP) can be used to optimise channel utilisation with upper bounds on handoff blocking probabilities as Quality of Service constraints for call admission control in a wireless cell in a Personal Communication System (PCS). However, this method is too time consuming and therefore it fails when state space and action space are large. In this paper, we apply a genetic algorithm approach to address the situation when the SMDP approach fails. We code call admission control decisions as binary strings. The coded binary strings are fed into the genetic algorithm, and the resulting binary strings are founded to be near optimal call admission control decisions. Simulation results from the genetic algorithm are compared with the optimal solutions obtained from linear programming for the SMDP approach. The results reveal that the genetic algorithm approximates the optimal approach very well with less complexity.