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Linear Quadratic Regulator (LQR) is one of the most interesting control techniques adopted as a control strategy in state feedback. These types of techniques achieve good results but suffer from the problem of trial and error involved in the computation of weight matrices. The trial and error technique leads to hard tuning of the LQR controller parameters. This of course will lead to difficulty in reaching the optimal system performance. The paper attempts to solve the above difficulty via the selection of the LQR weight matrices using Genetic Algorithm GA. This proposed solution will avoid the trail and error involved in the state feedback technique. The proposed solution has been adopted in the design of position controller of a robot arm and the results of computer simulation have shown that the proposed solution fulfill specifications, for minimum overshoot , settling and rising times. [ABSTRACT FROM AUTHOR]