An auto-navigation system with variant speed adaptability is developed to improve the robustness of the autonomous agricultural machinery. Based on a commercial agricultural tractor, New Holland 1404, an RTK-GNSS based autonomous navigation system is presented in this research. The system consists of a dual-antenna GNSS receiver with centimeter-level positioning accuracy, an on-board computer, an electronic steering wheel, a steering angle sensor, and so on. A vehicle control unit is designed to analyze the driver operations, to transmit the commands to actuators, and to broadcast tractor statuses following the ISO 11783 protocol. The control algorithm is modified from the pure pursuit path tracking method using a vehicle dynamic model with slip angle. The look-ahead distance of the pure pursuit method is adaptive to the vehicle speed. On the farmland at 4.5m/s speed limitation, the lateral error is about 3.3 cm. Experiments reveal that the proposed auto-navigation algorithm with adaptive look-ahead distance is robust to variant working conditions. In addition, consistent operation accuracy is achieved by the speed adaptive path tracking algorithm and updated vehicle parameters during headland turn. The navigation system is evaluated in auto-steering mode and fully autonomous mode. It has been proved to be a cost-efficient solution for controlling a conventional tractor.