Most obstacle avoidance control methods of the wheeled mobile robot(WMR) need to decelerate during the navigation, which affects the movement efficiency. The viability theory is used to WMR obstacle avoidance reactive control. Firstly affine nonlinear system model and constraints of WMR with non-homonymic constraint are analyzed. Then, by using the elastic boundary rising dimension and degradation of control model method, the system viability design is given. The optimization method is applied to the obtained controller of the robot for high-speed obstacle avoidance. Finally, simulation experiments show the effectiveness of the high speed WMR obstacle avoidance method.