The presence of fog has a significant adverse impact on driving. Reduced visibility due to fog obscures the driving environment and greatly affects driver behavior and performance. Lane-keeping ability is a lateral driver behavior that can be very crucial in run-off-road crashes under reduced visibility conditions. A number of data mining techniques have been adopted in previous studies to examine driver behavior including lane-keeping ability. This study adopted an association rules mining method, a promising data mining technique, to investigate driver lane-keeping ability in foggy weather conditions using big trajectory-level SHRP2 Naturalistic Driving Study (NDS) datasets. A total of 124 trips in fog with their corresponding 248 trips in clear weather (i.e., 2 clear trips: 1 foggy weather trip) were considered for the study. The results indicated that affected visibility was associated with poor lane-keeping performance in several rules. Furthermore, additional factors including male drivers, a higher number of lanes, the presence of horizontal curves, etc. were found to be significant factors for having a higher proportion of poor lane-keeping performance. Moreover, drivers with more miles driven last year were found to have better lane-keeping performance. The findings of this study could help transportation practitioners to select effective countermeasures for mitigating run-off-road crashes under limited visibility conditions.