This paper presents a self-tuning controller based on a quantum neural network and investigates the controller's characteristics for control systems. A multi-layer quantum neural network which uses qubit neurons as an information processing unit is utilized to design an adaptive-type self-tuning controller which conducts the training of the quantum neural network as an online process. As an example of designing the self-tuning controller, either a proportional integral derivative controller or a fuzzy logic controller is utilized as a conventional controller for which parameters are tuned by the quantum neural network. To evaluate the learning performance and capability of the adaptive-type quantum neural self-tuning controller, we conduct computational experiments to control the single-input single-output non-linear discrete time plant. The results of the computational experiments confirm both feasibility and effectiveness of the proposed self-tuning controller.