Traffic accidents on the expressways during the high speed driving are severe and more damaging, compared with other traffic accidents. There has been much effort to reduce the traffic accidents by seeking for the cause of the accidents. Apart from drunk driving and driving while drowsy caused by personal carelessness, one of the main causes of the accidents on the expressways is the limit to the straight-ahead. The straight-ahead is much affected by climate and topography. Existing research on this subject investigates the accidents during the driving on the expressways under bad weather, the accidents on the freeways with design problems regarding the topology and grade and the accident frequency varying with traffic volume. The current study suggests a model including precipitation and traffic volume at a time and aims at examining their impacts on the traffic accidents on the expressways by using a binomial logistic regression analysis. The data used were the traffic accident frequency per day over a year on each link of two expressways, Donghae and Yeongdong, which represent Yeongdong and Yeongseo regions of Gangwon Province. The results tell that precipitation and traffic volume significantly affect the occurrence of the traffic accidents. The accident occurrence is also significantly different between the two expressways and even more significantly different between links within each expressway. Further research topics were identified, including the distinction between rainfall and snowfall, the inclusion of mediating variables such as the limit to the straight-ahead due to the precipitation and the differentiation between the degrees of fatality of the traffic accidents.