This paper proposes a design method of self-tuning generalized minimum variance control based on on-demand type feedback controller. A controller, such as generalized minimum variance control (GMVC), generalized predictive control (GPC) and so on, can be extended by using coprime factorization. Then new design parameter is introduced into the extended controller, and the parameter can re-design the characteristic of the extended controller, keeping the closed-loop characteristic that way. Although strong stability systems can be obtained by the extended controller in order to design safe systems, focusing on feedback signal, the extended controller can adjust the magnitude of the feedback signal. That is, the proposed controller can drive the magnitude of the feedback signal to zero if the control objective was achieved. In other words the feedback signal by the proposed method can appear on demand of achieving the control objective. Therefore this paper proposes on-demand type feedback controller using self-tuning GMVC for plant with uncertainty. A numerical example is shown in order to check the characteristic of the proposed method.