This paper presents a nonlinear model predictive tracking control scheme for a six-wheeled nonholonomic unmanned ground vehicles (UGVs). It is employed as a high-level guidance control with kinematic approximation for UGV motion. A nonlinear model predictive control algorithm solves trajectory planning and optimal control problems by sequentially solving an online numerical optimization problem. The optimal control inputs for the UGV are obtained with a gradient descent optimization algorithm considering constraints of UGV motion as well as its input constraints. The characteristics of the proposed controller in terms of tracking performance and collision avoidance were investigated. The real-time performance of the proposed numerical optimization algorithm was verified with an experimental six-wheeled UGV platform in indoor and outdoor environments.