A single-wheel mobile robot called Gyrocycle has been developed for carrying a human driver. Since a single-wheel mobile robot carries a human driver, the size and weight are designed to be larger compared with other single-wheel mobile robots. To maximize the balancing force, Gyrocycle is designed to have two flywheels required to be synchronized. Since a simple PD control lacks the robusteness, a radial basis function (RBF) neural network controller is added at the reference to compensate for the uncertainies when external disturbances are present. Experimental studies of balancing performances are conducted to verify the performance by the neural network controller.