Limit cycle oscillation (LCO) is an isolated periodic solution of nonlinear system dynamics. Since desirable band of frequencies of LCO varies from system to system, we often need to change our systems LCO frequency to a desired one. This paper presents method for the determination of LCO fre- quency for linear relay feedback system. The linear relay feedback system is a simple nonlinear system appropriate for the study of LCO phenom- ena. We present how to design a lead compensator to manipulate LCO frequency. Based on the theories of piecewise linear systems and Poincare map, we have solved for the parameters of the lead compensator for a new desired LCO frequency. Finally, we numerically check for the local and global stability of the new LCO. Several examples of linear relay feedback systems demonstrate that the lead compensator of our design determines LCO frequency exactly as we want, maintaining the local and global stabi.