Linear RankSVM is one of the widely used methods for learning to rank. Although using Order-Statistic Tree (OST) and Trust Region Newton Methods (TRON) are effective to train linear RankSVM on CPU, it becomes less effective when dealing with large-scale training data sets. Furthermore, linear RankSVM training with L2-loss contains quite amount of matrix manipulations in comparison with that with L1-loss, so it has great potential for achieving parallelism on GPU. In this paper, we design efficient parallel algorithms on GPU for the linear RankSVM training with L2-loss based on different queries. The experimental results show that, compared with the state-of-the-art algorithms for the linear RankSVM training with L2-loss on CPU, our proposed parallel algorithm not only can significantly enhance the training speed but also maintain the high prediction accuracy.