Unicycle robot stabilized by a lateral pendulum is an underactuated unstable system which is very challenging from control perspective. Its control challenge arises from difficulty in lateral stabilization, absence of direct control input for the control of turning motion and couplings among the longitudinal, lateral and turning dynamics. Research on this robot is mainly based on linear dynamic model which is developed by initially assuming that the longitudinal and lateral dynamics are completely decoupled. Such method results in the absence of turning dynamic model and, therefore, accurate control of turning motion is not possible. However, as a type of mobile robots, lateral-pendulum unicycle robot must have turning-motion-control capability, so that navigational control tasks such as path following can be achieved. In this paper, we present a control structure based on gain scheduling which can steer the robot and maintain its lateral stability at the same time. This control structure consists of three controllers namely (1) longitudinal controller, (2) lateral controller and (3) turning controller. Longitudinal controller is responsible for the generation of forward motion according a pre-set reference by means of wheel actuation. Taking into account the robot's forward speed, turning controller computes the reference for lean angle, which is then acted upon by lateral controller through pendulum actuation. The performance of this control structure is investigated through numerical simulation.