This paper deals with the control of the memristor-based simplest chaotic circuit by means of only one-state controller. Three distinct control techniques, namely linear feedback control, sliding mode control, and nonlinear control, are examined for the control. Routh-Hurwitz stability criteria are used for constructing the linear feedback and sliding mode gains. Lyapunov function is used for ensuring the global asymptotic stability of the system with the nonlinear controller. Numerical simulations are demonstrated not only to validate the theoretical analyses, but also to compare the control results. They have shown that even if one-state controller is used, all the methods are effective for controlling the memristor-based simplest chaotic circuit. However, the control is observed in a better time period with the sliding mode controller.