Abstarct: In this thesis, One-wheel vehicle with four degrees of freedom for the first time as a non-linear and without linearization is modeled. In all studies, vehicle model have two or three degrees of freedom due to motion limitations of a single wheel. In this thesis, the model by using special mechanism for a wheel that provides more degrees of freedom is presented. Equations of motion one-wheel vehicle by using Lagrange method and sequential Euler angles are calculated. Four equation of motion are coupled and nonlinear and more complicated to compare vehicle model with three degrees of freedom. This vehicle is included passenger seating, two motor and one Omni directional wheels which consists of a number of small wheel and a large wheel. Four degrees of freedom of the system are: the pitch angle which the axis of rotation of the big wheel, roll angle which describe the vehicle inclination, the angle of inclination of the passenger seating cause moving forward –backward and rotation angle of small wheels cause moving left – right. Motors are located on the passenger seating and reaction torque generated by the motor is applied to body and chassis of passenger seating. There is uncertainty in computing the geometric parameters of the system due to measurement error. Nonlinear adaptive control method is used to overcome the uncertainties of system and control it. Also by using Lyapunov stability method, the stability of the vehicle is investigated and ensured. Adaptive control method is used Self-Tuning adaptive controllers which performance improved by making correction in it. Due to the complex structure equations using a new idea that contains an inner loop, torque control signal is calculated and sent to the motor. Finally, the equations of motion are simulated in MATLAB-Simulixnk and after verification and comparison with the physics and modeling is acknowledged. To verify the performance of the adaptive control method, its results are compared with a PD control method. Adaptive control works well and compensates the inclination of vehicle to forward-backward and sideway and ensures stability.