Although recent advancements in end-to-end learning-based link prediction (LP) methods have shown remarkable capabilities, the significance of traditional similarity-based LP methods persists in unsupervised scenarios where there are no known link labels. However, the selection of node features for similarity computation in similarity-based LP can be challenging. Less informative node features can result in suboptimal LP performance. To address these challenges, we integrate self-supervised graph learning techniques into similarity-based LP and propose a novel method: Self-Supervised Similarity-based LP (3SLP). 3SLP is suitable for the unsupervised condition of similarity-based LP without the assistance of known link labels. Specifically, 3SLP introduces a dual-view contrastive node representation learning (DCNRL) with crafted data augmentation and node representation learning. DCNRL is dedicated to developing more informative node representations, replacing the node attributes as inputs in the similarity-based LP backbone. Extensive experiments over benchmark datasets demonstrate the salient improvement of 3SLP, outperforming the baseline of traditional similarity-based LP by up to 21.2% (AUC).