Graph neural networks (GNNs) have achieved promising performance on semantic dependency parsing (SDP), owing to their powerful graph representation learning ability. However, training a high-performing GNN-based model requires a large amount of labeled data and it is prone to over-fitting in the absence of sufficient labeled data. To address this drawback, we propose a syntax-guided graph contrastive learning framework to pre-train GNNs with plenty of unlabeled data and fine-tune pre-trained GNNs with few-shot labeled SDP data. Through extensive experiments conducted on the SemEval-2015 Task 18 English dataset in three formalisms (DM, PAS, and PSD), we demonstrate that our framework achieves promising results when few-shot training samples are available. Furthermore, benefiting from the pre-training process, our framework exhibits notable advantages in the out-of-domain test sets.