Although car-following model is one of the core components of traffic flow theory, the characteristics of left turning car-following behavior in turning process at signalized intersections has not been examined with field data yet. Aiming at this point, a left-turn car-following experiment at signalized intersection was designed. Based on high precision GPS and Mobil GIS system, the data of car-following behavior was collected, and the time-varying law and distribution characteristics of left-turn car-following speed at signalized intersections with different turning radius were analyzed. On the basis of Full Velocity Difference (FVD) model, considering the asymmetry of driver's response to acceleration and deceleration of the leading car, an Improved FVD (IFVD) model was developed, and the parameters of the model were calibrated by genetic algorithm. Finally, taking the acceleration of the following car as the test index, the accuracy of the acceleration and deceleration process of the IFVD model were analyzed and evaluated by using the real-world data. This study found that (1) the average speed of the left-turning car-following vehicle increases with the turning radius of signalized intersection; (2) the highest frequency of car-following speed increases with the increase of turning radius; and (3) the IFVD model can better describe the left turn car-following process at signalized intersections, and the driver’s response sensitivity to the deceleration behavior of the front vehicle is stronger than that of the acceleration.