Many practical design problems arise in which the desired system performance constraints cannot be accommodated by the available optimizing theoretic techniques. Genetic algorithms (GA) offer a numerical search method, which does not require a statement of the mathematical relationship between the performance criteria and the parameter update rule. The objective of this paper is to demonstrate that GA provides a method of optimizing control system with analytically intractable constraints. A linear guided bomb airframe and actuator state space model is developed with linear feedback controller and implemented in a discrete time simulation. A genetic algorithm is constructed to optimize the linear controller parameters, with respect to a weighted linear quadratic performance index. Additional performance constraints are then imposed to meet rise time, peak actuator effort, and settling error specifications. Computer simulation results show that the genetic algorithm provides good convergence to near optimal controller designs for each successive combination of constraints.