The traditional weighted multiple instance learning based online object tracking methods often use the Euclidean distance between the centers of the bounding boxes of the target and the instance to weight the instances in the positive bag, which can not effectively measure the contribution degree of the instances of the positive and negative bags and easily causes the object drifting problem. This paper proposes a generalized intersection over union based online weighted multiple instance learning algorithm (named GIoU-WMIL) for object tracking. This algorithm introduces a novel generalized intersection over union (GIoU) to calculate the overlap degree between the bounding boxes of the target and each instance in the bags, in order to effectively measure the contribution of the different instances. Furthermore, a new objective function is designed by employing the GIoU-based weights of all the instances in the positive and negative bags. Experiments show that the proposed algorithm has the good robustness and accuracy on several challenging video sequences.