Extracting semantic relations between entities is an important step towards automatic text understanding. In this paper, we propose a novel Semi-supervised Convolution Graph Kernel (SCGK) method for semantic Relation Extraction (RE) from natural English text. By encoding sentences as dependency graphs of words, SCGK computes kernels (similarities) between sentences using a convolution strategy, i.e., calculating similarities over all possible short single paths on two dependency graphs. Furthermore, SCGK adds three semi-supervised strategies in the kernel calculation to enable soft-matching between (1) words, (2) grammatical dependencies, and (3) entire sentences, respectively. From a large unannotated corpus, these semi-supervision steps learn to capture contextual semantic patterns of elements inside natural sentences, and therefore alleviate the lack of annotated examples in most RE corpora. Through convolutions and multi-level semi-supervisions, SCGK provides a powerful model to encode both syntactic and semantic evidence which are important for effectively recovering the relational patterns of interest. We perform extensive experiments on five RE benchmark datasets which aim to identify interaction relationships from biomedical literature. Our results demonstrate that SCGK achieves the state-of-the-art performance on the task of semantic relation extraction.