Simple and efficient geometric controllers, like Pure-Pursuit, have been widely used in various types of autonomous vehicles to solve tracking problems. In this paper, we have developed a new pursuit method, named CF-Pursuit, which has been based on Pure-Pursuit but with certain differences. In CF-Pursuit, in order to reduce fitting errors, we used a clothoid C1 curve to replace the circle employed in Pure-Pursuit. This improvement to the fitting method helps the Pursuit method to decrease tracking errors. As regards the selection of look-ahead distance, we employed a fuzzy system to directly consider the path's curvature. There are three input variables in this fuzzy system, 6 mcurvature, 9 mcurvature and 12 mcurvature, calculated from the clothoid fit with the current position and the goal position on the defined path. A Sugeno fuzzy model was adapted to output a reasonable look-ahead distance using the experiences of human drivers as well as our own tests. Compared with some other geometric controllers, CF-Pursuit performs better in robustness, cross track errors and stability. The results from field tests have proven the CF-Pursuit is a practical and efficient geometric method for the path tracking problems of autonomous vehicles.