This study aims to build the adaptive sliding mode control based on radial basis function neural network, thereby offering online training algorithm allows self-adjusting controller parameters according variation characteristics of nonlinear dynamic. The controller based on radial basis function network structure that is trained online using Quasi-Newton method, this method for quadratic convergernce rate is faster and more precise than the traditional Gradient Descent algorithm. Training algorithm based on radial basis function network to approximate the Hessian matrix of each training period and apply the algorithms Broyden, Fletcher, Goldfarb and Shanno to update weights in the neural network. Testing simulation through MATLAB® and experiment with Omni- directional mobile robots. The process modeling results demonstrate that the RBF trained by BFGS algorithm are fast, reliable, and accurate.