Changes in driving behavior caused by reduced visibility in fog can lead to crashes. To improve driving safety in fog weather, a fog warning system based on connected vehicle (CV) technology is proposed. From the perspective of human factors, this study evaluates the driving safety based on drivers’ speed change under different fog levels (i.e., no fog, light fog, and heavy fog) and different technical levels (i.e., normal, with a dynamic message sign (DMS), and with a human-machine interface (HMI)). The driving behavior data were collected by a driving simulation experiment. The experimental road was divided into three zones: clear zone, transition zone, and fog zone. To quantify the change of vehicle speed comprehensively, the speed and acceleration were selected. Meanwhile, the vehicle speed safety entropy and acceleration safety entropy were proposed based on sample entropy theory. Furthermore, the changes of each index in different zones were analyzed. The results show that the use of fog warning system can improve speed stability and driving safety in fog zones and can make the driver decelerate in advance with a smaller deceleration before entering the fog zones. The higher the technical level is, the earlier the driver decelerates. Under the condition of light fog, the fog warning system with HMI has a better effect in terms of improving speed stability, while under the condition of heavy fog, there is little difference between the two technical levels. In general, this study proposed a novel safety evaluation index and a general evaluation method of the fog warning system.