This article designs a PID sliding mode controller based on new Quasi-sliding mode (PID-SMC-NQ) and radial basis function neural network (RBFNN) for Omni-directional mobile robot. This is holonomic vehicles that can perform translational and rotational motions independently and simultaneously. The PID-SMC is designed to ensure that the robot's actual trajectory follows the desired in a finite time with the error converges to zero. To decrease chattering phenomena around the sliding surface, in the controller robust term, this paper uses the tanh (hyperbolic tangent) function, so called the new Quasi-sliding mode function, instead of the switch function. The RBFNN is used to approximate the nonlinear component in the PID-SMC-NQ controller. The RBFNN is considered as an adaptive controller. The weights of the network are trained online due to the feedback from output signals of the robot using the Gradient Descent algorithm. The stability of the system is proven by Lyapunov's theory. Simulation results in MATLAB/Simulink show the effectiveness of the proposed controller, the actual response of the robot converges to the reference with the rising time reaches 307.711 ms, 364.192 ms in the x-coordinate in the two-dimensional movement of the robot, the steady-state error is 0.0018 m and 0.00007 m, the overshoot is 0.13% and 0.1% in the y-coordinate, and the chattering phenomena is reduced.