This study presents an adaptive-type controller based on a quantum neural network and investigates its characteristics for control systems. A multi-layer quantum neural network which uses qubit neurons as an information processing unit is utilized to design three types of the adaptive-type quantum-neural-network-based controllers which conduct the learning of the quantum neural network as an online process: a direct controller, a parallel controller and an indirect controller. Computational experiments to control the single-input single-output non-linear discrete-time plant are conducted to evaluate the learning performance and capability of quantum neural controllers. The results of the computational experiments confirm the feasibility and effectiveness of adaptive-type quantum neural controllers.