<p>This work focuses on global minimum time trajectory planning for track racing considering curvature and distance based on offline high-precision map of track. Offline mapping of track, post processing and a new gridding method are firstly introduced. Then according to the requirement of quadratic programming method, the sum of discrete squared distance and the sum of discrete squared curvature are derived respectively, which are then combined together by a weight coefficient to constitute the objective function of minimum time trajectory. Drivable curbs, size of vehicle and safe distance are considered in constraint conditions in order to make full use of the width of track. With objective function and constraint conditions, quadratic programming method is used to calculate and iterate a smooth and reasonable trajectory. Petrol and electric racecars, different driver models and different trajectories are simulated in CarSim. Results show that conspicuous improvement can be obtained if using drivable curbs, and the minimum time trajectories for different vehicles and drivers display significant difference.</p>