The aim of this research is to develop an adaptive control system of a two-wheeled balancing robot based on a reference model and the second Lyapunov approach. Solving this problem, the following questions are considered: 1) a mathematical model of the robot reference dynamics is developed, 2) using the optimal control theory, a calculation of LQ controller parameters is made, 3) applying the second Lyapunov method, an algorithm to adjust the parameters of such controller is proposed. The step size is calculated in accordance with the proposed formula and depends on the current and previous setpoint values of one of the robot state coordinates. A real balancing robot and its model are used to conduct experiments, over the course of which the mass of the robot is increased by several times. The obtained results show that, despite the robot non-stationarity, the developed adaptive control system is able to follow the reference model output keeping the transient quality close to the desired one.