A radial basis function neural network (RBFNN) is a branch of neural network which performs good to control the dynamics system. Several researchers have proposed many approaches to train RBFNN such as Gradient Descent (GD), Newton’s method, Conjugate Gradient, Quasi-Newton, Levenberg Marquardt. This paper presents the Quasi-Newton method with Broyden – Fletcher – Grodfarb – Shanno (BFGS) for online training the RBFNN. The Quasi-Newton method was studied as one of the most effect optimization algorithms based on the gradient descent. After being trained, the RBFNN is applied to control Omni-directional mobile robot based on sliding mode controller. The RBFNN is considered as an adaptive controller. The simulation results in MATLAB Simulink show that the proposed algorithm is efficient, the response of adaptive sliding mode controller with Quasi-Newton algorithm converge to reach the trajectory.