Auto-driving is an important technology development direction, and pedestrian detection is an indispensable key technology to achieve this goal, which belongs to the hot research field of computer vision. The main methods in the field of pedestrian detection are based on statistical learning, but in practice, this method has some problems such as incomplete negative sample data set and complex classifier. To solve these problems, a support vector domain data description and Histogram of oriented gradients pedestrian detection algorithm are proposed, hog and SVDD were used to learn and extract the features of the data set samples, and the penalty terms were solved by the equation. Joseph-louis Lagrange operator was introduced to reduce the complexity of the classifier, furthermore, the generalization degree between the training set of negative samples and the real scene is enhanced. First, a multi-scale candidate sample is generated by using the sliding window. Secondly, Histogram of oriented gradients statistics is used to extract the features of the image samples. Thirdly, based on the complete positive samples and the support vector domain, a single classifier with positive samples is trained to detect pedestrians. Experiments show that compared with the traditional pedestrian detection method based on statistical learning, the Hog and SVDD pedestrian detection algorithm has lower false positive rate and less total training samples, it has good generalization ability and certain practical research value, but needs more positive samples for training.