Semantic textual similarity is a fundamental task in text mining and natural language processing (NLP), which has profound research value. The essential step for text similarity is text representation learning. Recently, researches have explored the graph convolutional network (GCN) techniques on text representation, since GCN does well in handling complex structures and preserving syntactic information. However, current GCN models are usually limited to very shallow layers due to the vanishing gradient problem, which cannot capture non-local dependency information of sentences. In this paper, we propose a GCNs-based context-aware (GCSTS) model that applies iterated GCN blocks to train deeper GCNs. Recurrently employing the same GCN block prevents over-fitting and provides broad effective input width. Combined with dense connections, GCSTS can be trained more deeply. Besides, we use dynamic graph structures in the block, which further extend the receptive field of each vertex in graphs, learning better sentence representations. Experiments show that our model outperforms existing models on several text similarity datasets, while also verify that GCNs-based text representation models can be trained in a deeper manner, rather than being trained in two or three layers.