To further improve the performance and the self-learning ability of GCNs, in this paper, we propose an efficient self-supervised learning strategy of GCNs, named randomly removed links with a fixed step at one region (RRLFSOR). In addition, we also propose another self-supervised learning strategy of GCNs, named randomly removing links with a fixed step at some blocks (RRLFSSB), to solve the problem that adjacent nodes have no selected step. Experiments on transductive link prediction tasks show that our strategies outperform the baseline models consistently by up to 21.34% in terms of accuracy on three benchmark datasets.